Research Article An Empirical Study of the Effect of

Research ArticleAn Empirical Study of the Effect of Investor Sentiment onReturns of Different Industries

Chuangxia Huang12 Xin Yang3 Xiaoguang Yang23 and Hu Sheng4

1 School of Mathematics and Computing Science Changsha University of Science and Technology Changsha 410114 China2 Academy of Mathematics and Systems Science Chinese Academy of Science Beijing 10090 China3 School of Economics and Management Changsha University of Science and Technology Changsha 410114 China4 School of Business Central South University Changsha Hunan 410083 China

Correspondence should be addressed to Hu Sheng csu shenghu163com

Received 11 December 2013 Accepted 12 February 2014 Published 17 April 2014

Academic Editor Fenghua Wen

Copyright copy 2014 Chuangxia Huang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Studies on investor sentiment are mostly focused on the stock market but little attention has been paid to the effect of investorsentiment on the return of a specific industry This paper constructs a proxy variable to examine the relationship between investorsentiment and the return of a specific industry using the Principle Component Analysis and finds that investor sentiment ispositively correlated with the industry return of the current period and negatively correlated with that of one lag period we classifyinvestor sentiment as optimistic state and pessimistic state and find that optimistic investor sentiment has a positive effect on stockreturns of most industries while pessimistic investor sentiment has no effect on them this paper further builds a two-state Markovregime switching model and finds that sentiment has different effect on different industries returns on different states of market

1 Introduction

Classical financial theory believes that the market is efficientall investors have perfect rationalities and the security pricehas adequately reflected all the information in the marketso the asset price cannot be affected by investor sentimentHowever with the development of the financialmarketmanyldquoanomaliesrdquo cannot be explained Many scholars began todoubt the assumption of market efficiency and behavioralfinance emerged Behavioral finance rejected the assumptionof investorsrsquo perfect rationality and holds that investors tendto be affected by their own sentiment whilemaking decisionswhich leads to bias of irrationalities in investment decisionConsequently investor sentiment may be a systematic riskfactor which affects stock returns Bradford De Long et al[1] proved that investor sentiment is an intrinsic factor whichaffects the equilibrium price of the stock with a noise tradermodel

Currently many scholars try to explore the relationshipbetween investor sentiment and the stock return in terms ofinvestor sentiment Lee et al [2] proved that excess returns

are contemporaneously positively correlated with shifts insentiment and the magnitude of bullish (bearish) changes insentiment leads to downward (upward) revisions in volatilityand higher (lower) future excess returns Brown and Cliff [3]found that investor sentiment cannot predict future returnin the short run and it is negatively correlated with returnsof the next one to three years Baker and Wurgler [4] arguethat market-wide sentiment should exert stronger impactson stocks that are difficult to value and hard to arbitrageLemmon and Portniaguina [5] find that investor sentimenthas a negative effect on value stocks but has no significanteffect on growth stocks Stambaugh et al [6] illustrate thata broad set of anomalies are stronger following high levels ofsentiment and the short leg of each strategy ismore profitablefollowing high sentiment but sentiment exhibits no relationto returns on the long leg of the strategies Ben-Rephaelet al [7] pointed out that investor sentiment is positivelycorrelated with the excess return of the market in the sameperiod and negatively correlated with the excess return oflater periods Baker et al [8] proved that global sentiment isa contrarian predictor of country-level returns Both global

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 545723 11 pageshttpdxdoiorg1011552014545723

2 Mathematical Problems in Engineering

and local sentiments are contrarian predictors of the timeseries of cross-sectional returns within markets Wang andSun [9] showed that investor sentiment does not only affectthe returns of Shanghai and Shenzhen stockmarkets but alsoreversely corrects return fluctuations of these two marketsto a large extent Study by Huang [10] finds that there is adistinct cross-sectional effect between the investor sentimentindex and the expected return of the market and the effectis reflected in return indices for different industries with thelargest effect on the information industry and the least effecton the transportation industry

Some scholars classify investor sentiment as the opti-mistic state and the pessimistic state in order to examinethe effect of investor sentiment on the return of a specificindustry For example Zhang and Yang [11] adopt GARCH-M Model to prove that institutional investor sentiment hasa great effect on stock returns and sentiment rise has agreater effect on stock returns than sentiment decline Chiand Zhuang [12] demonstrated investor sentiment affectsstock returns significantly and the effect of optimistic sen-timent is greater than that of pessimistic sentiment Besidesextreme sentiment has a special predictive power in the stockmarket Lu and Lai [13] showed that investor sentiment hasa significant effect on the Shanghai composite index Whenthe market is in a rising stage investor sentiment is moreoptimistic and more investors enter the market when themarket is in a declining stage investor sentiment is relativelypessimistic and investors will wait to enter the market

The state of the financial market (bearish or bullish)changes accordingly with the continuous change in the finan-cial market and the adjustment of macroeconomic policywhich will lead to corresponding changes of the coefficientsfor the econometric model for the return of an industryOne of the models to capture this kind of coefficient changeis the Markov switching regime model with state changeHamilton [14] introduced for the first time theMarkov regimeswitching model into a variable structure model and studiedthe effect of the cyclic changes of the US economy on theactual output from 1953 to 1984 Later a large number ofresearchers adopted the Markov regime switching model tocharacterize endogenic structural changes such as Lanne etal [15] Farmer et al [16] and Chen et al [17] This paperattempts to verify the bull and bear market using the two-stateMarkov regime switchingmodel On this basis it furtherexamines the changes in the effect of investor sentiment onreturns of different industries in different market states

Previous studies showed that investor sentiment signifi-cantly affects stock returns Which kinds of industryrsquos stocksare more easily affected by investor sentiment Are thereany differences between their effects of the optimistic andthe pessimistic states on returns of an industry What is thedifference between the effects of investor sentiment on thereturn of an industry at different market states Aiming atthese questions this paper will conduct close explorationsAnd my paperrsquos main contribution is to set a two-stateMarkov regime switching model to find that sentiment hasdifferent effect on different industries returns on differentstates of marketThe remaining part of this paper is arrangedas follows the second part is for the index construction of

investor sentiment the third part is an empirical study andthe fourth part is the conclusion

2 Proxy Index Construction ofInvestor Sentiment

21 The Selecting of Proxy Indicator of Investor SentimentAt present there are two measures for investor sentimentmdashthe direct approach and the indirect approach The directapproach is rather subjective and can get only a portionof investor feedbacks Therefore most investor sentimentmeasurements adopt the index in Baker and Wurgler study[4] which selects these six variablesmdashthe average closed-endfund discount (CEFD) NYSE share turnover (TURN) thenumber on IPOs (NIPO) average first-day returns on IPOs(RIPO) the equity share in new issues and the dividendpremium to form an investor sentiment variable based onthe Principal Component Analysis Considering the charac-teristics of the Chinese stock market and the availability ofdata this paper selects CEFD NIPO RNIPO the numberof new investor accounts for A shares (NIA) and Shanghaishare turnover (TURN) to form a proxy variable for investorsentiment based on the Principal Component Analysis Thesamples are monthly data from the Resset database duringJanuary 2005 to January 2013 (httpwwwressetcn)

(1) CEFD CEFD is the ratio of the difference between thenet asset value (NAV) and unit price of the closed-end fundto NAV Lee et al [18] find that investor sentiment canbe measured by CEFD and it also gives a comprehensiveexplanation to the closed-end fund discount puzzle Wuand Han [19] show that CEFD can be a proxy variable forinvestor sentimentWhen there is a high CEFD stockmarketinvestors lack confidence and their sentiment is low

The calculation formula is

CEFD119905=

sum

119899

119894=1((119875119894119905minusNAV

119894119905) (NAV

119894119905))

119899

(1)

where119875119894119905is the closing price of fund 119894 inmonth 119905 NAV

119894119905is the

last NAV published in month 119905 and 119899 represents the numberof the selected funds

(2) NIPO Initial public offering (IPO) is the process forthe enterprise to firstly issue stocks to investors in the stockexchange for the first time to raise funds for its developmentWhen the market sentiment runs high the stock price willgrow and the pace of IPOs will speed up leading to moreIPOs during such high market sentiment period On thecontrary when the market is in low sentiment the stockmarket will slow down or even suspend the issuing of newstocks Empirical evidence presented by Baker and Wurgler[4] finds that the number of IPOs (NIPO) is a good proxyvariable for investor sentiment

(3) RIPO RIPO denotes the return on the IPO in the firsttrading day namely the percentage of the closing price to theoffering price When the market sentiment is high investorswill have a greater interest in the new stock thus resultingin higher return on the IPO (RIPO) Otherwise low investor

Mathematical Problems in Engineering 3

Table 1 Descriptive statistics of each index

Mean Standard deviation Kurtosis Skewness JB statisticsCEFD 0241111 0121486 0380086 1908905 7147080lowastlowast

NIPO 1322271 9999192 0688533 2208237 1019792lowastlowastlowast

RIPO 0921679 0876651 2985041 1661689 8934568lowastlowastlowast

TURN 0376856 0233725 1287418 4410218 3483308lowastlowastlowast

NIA 1080212 1063835 1897781 7143569 1276175lowastlowastlowast

The correlation of indexesCEFD NIPO RIPO TURN NIA

CEFD 1NIPO minus0667911lowastlowastlowast 1RIPO 0220840lowastlowast minus0368060lowastlowastlowast 1TURN 0418940lowastlowastlowast minus0279498lowastlowastlowast 0291517lowastlowastlowast 1NIA minus0138380 0122912 0343842lowastlowastlowast 0610424lowastlowastlowast 1Notes lowastlowastlowast lowastlowast and lowast denote respectively significance at the significance level of 1 5 and 10 similar hereinafter

Table 2 Correlation between investor sentiment and ten variables

CEFD119905

NIPO119905

RIPO119905

TURN119905

NIA119905

CEFD119905minus1

NIPO119905minus1

RIPO119905minus1

TURN119905minus1

NIA119905minus1

SentRAW119905

0761 minus0700 0565 0745 0378 0766 minus0723 0559 0740 0333

sentiment will produce a low interest in the IPOs leading toa decrease in RIPO Baker and Wurgler [4] find that RIPOis a good proxy variable for investor sentiment Chineseresearchers Wu and Han [19] find that the discount and thepremium of IPO can be used to explain investor sentiment

(4) NIA The number of new investment accounts (NIA)reflects investorsrsquo market demand in the stock market Wheninvestor sentiment is high the enthusiasm to enter themarketwill rise and the number of investment accounts will increaseaccordingly otherwise the number of investment accountswill decrease Wu and Han [19] and Zhang and Yang [11] allsuggest that NIA can be used as a good proxy variable forinvestor sentiment

(5) TURNThe turnover rate (TURN) of a stock is the fractionsoldwithin a certain period of timeWhen investor sentimentis high they actively participate in trades resulting in highTURN otherwise the decrease in market participation willlead to low TURN Wu and Han [19] and Zhang and Yang[11] believe that TURN can be a proxy variable for investorsentiment TURN data in this paper is the weighted monthlyaverage turnover of A shares

According to the correlation analysis of each index inTable 1 each index is correlated to one another in a rathercomplicated manner For example a negative correlationexists between all these pairs of proxy variablesmdashCEFD andNIPO CEFD and NIA NIPO and RIPO and NIPO andTURN

22 The Constructing of Investor Sentiment Index This paperadopts Baker and Wurglerrsquos [4] approach to forming aninvestor sentiment proxy index We start by estimating thefirst principal component of the five proxies and their lagsThis gives us a first-stage indexwith ten loadings one for each

of the current and lagged proxies The synthesized sentimentindexes are presented as follows (the cumulative contributionrate of the first five components is 8706)

SentRAW119905

= 0372646CEFD119905minus 0342926NIPO

119905

+ 0276802RIPO119905+ 0364866TURN

119905

+ 0185272NIA119905+ 0375499CEFD

119905minus1

minus 0354266NIPO119905minus1

+ 0273913RIPO119905minus1

+ 0362383TURN119905minus1

+ 0163127NIA119905minus1

(2)

We then compute the correlation between the first-stageindex and the current and lagged values of each of the proxiesFinally we construct Sent

119905as the first principal component of

the correlation matrix of five variables of each proxyrsquos lead orlag whichever has the higher correlation with the first-stageindex

Table 2 shows that each proxyrsquos lead or lag with highercorrelation coefficient is CEFD

119905minus1 NIPO

119905minus1 RIPO

119905 TURN

119905

and NIA119905 We analyze these five indexes with the Prin-

ciple Component Analysis we choose the first principlecomponent (the cumulative contribution rate of the firstthree components reaches 9017) and we get the followingsentiment composite index Sent

119905

Sent119905= 0477612CEFD

119905minus1minus 0474077NIPO

119905minus1

+ 0436559RIPO119905+ 0522063TURN

119905

+ 0289835NIA119905

(3)

Figure 1 shows that investor sentiment began to rise withmore enthusiasm in market participation in April 2005 whenpilot separation reform projects started in China From 2006


Table 3 Return statistics of each industry

Industry Mean Standard deviation Kurtosis Skewness JB statistics ADF-tFarming forestry animal husbandry and fishery 0006894 0097631 minus0214655 3532165 1889504 minus7737645lowastlowastlowast

Extractive industry 0003295 0111691 0305372 3557856 2765355 minus6799325lowastlowastlowast

Chemical industry 0003431 0085623 0094045 3258920 0413938 minus6474173lowastlowastlowast

Ferrous metals minus0002846 0104951 0281164 3749400 3547828 minus2596785lowastlowastlowast

Nonferrous metals 0006204 0126077 minus0060071 3507858 1100764 minus6442558lowastlowastlowast

Construction materials 0002747 0096980 0356129 3747072 4306106 minus6566892lowastlowastlowast

Mechanical installation 0002188 0096631 minus0139295 2820706 0443606 minus6725198lowastlowastlowast

Electronics minus0000460 0103672 minus0260335 3074738 1118260 minus6993854lowastlowastlowast

Transportation equipment 0006274 0103173 minus0127551 3037118 0268588 minus5715664lowastlowastlowast

Information equipment 0000262 0099586 minus0222712 2953698 0810538 minus6880790lowastlowastlowast

Household appliances 0004821 0095675 minus0193469 3177335 0732221 minus6330048lowastlowastlowast

Food and beverage 0013467 0085772 minus0040146 3970131 3829889 minus7478488lowastlowastlowast

Textile and garment 0003287 0100715 0469081 4824239 1700731lowastlowastlowast minus6417958lowastlowastlowast

Light manufacturing 0000639 0099941 minus0258313 3807337 3713056 minus6610410lowastlowastlowast

Biopharmaceuticals 0009660 0086362 0170174 3313894 0866395 minus7461154lowastlowastlowast

Public utility minus0000795 0079753 0362636 4353036 9525104lowastlowastlowast minus6586849lowastlowastlowast

Transportation minus0004077 0081682 0085057 3716854 2193894 minus6268708lowastlowastlowast

Real estate 0004154 0098869 minus0118194 3631311 1836662 minus5748892lowastlowastlowast

Financial service 0000202 0090827 0024149 4098793 4889115lowast minus3433203lowastlowast

Business and trade 0003520 0091366 0036296 3540816 1203414 minus6418831lowastlowastlowast

Catering and tourism 0007037 0100273 minus0376900 3413545 2987743 minus6964831lowastlowastlowast

Information service 0003905 0083502 minus0207364 3681743 2573628 minus7372482lowastlowastlowast

General industry 0002546 0104683 0200064 3862630 3654610 minus6265502lowastlowastlowast

Notes lowastlowastlowast lowastlowast and lowast denote respectively significance at the significance level of 1 5 and 10

minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

Jan-05

Jul-0

5

Jan-06

Jul-0

6

Jan-07

Jul-0

7

Jan-08

Jul-0

8

Jan-09

Jul-0

9

Jan-10

Jul-1

0

Jan-11

Jul-1

1

Jan-12

Jul-1

2

Jan-13

Figure 1 Investor sentiment

to the end of 2007 investor sentimentwas pushed to a summitwith a lot of good news such as continuous improvement incorporate performance and the abolition of constrictions onforeign investment and a big bull market emerged in Chinesestockmarkets However negative influence of subprime crisisin the United States spreads to domestic investors leadingto market index slump and pessimistic attitude towardstock markets By way of selecting proxy index of investorsentiment and synthesizing new proxy index with principalcomponents investor behavior in the stock market can bebetter characterized Thus the new proxy index is morereasonable to a certain extent

3 Empirical Study

This paper adopts Wind Information monthly data fromJanuary 2005 to January 2013 and divides industries into 23

categories The monthly return of a specific industry is 119903119894119905

=

ln119901119894119905

minus ln119901119894119905minus1

where 119901 is the closing price of industry 119894

in month 119905 The descriptive statistics of each industry arepresented in Table 3

Table 3 shows that biopharmaceuticals farming forestryanimal husbandry fishery nonferrous metals catering andtourism and transportation equipment have high monthlyaverage returns with mean value of each above 0006 amongwhich the highest one is that of biopharmaceuticals andthe monthly average returns of transportation ferrous metalelectronics public utility and general industry are relativelylow with each mean value less than zero among whichthe lowest one is the stocks of transportation In terms ofindustry fluctuations nonferrous metal presents the widestrange because it is closely related to industries of large metaldemand such as real estate autoindustry and shipbuildingindustry These industries presented a cycle from prosperityto depression during the period from 2005 to 2013 thusleading to awide range of fluctuations of nonferrous industry

31 The Relationship between Market Sentiment and Return ofa Specific Industry For the concurrent effect of sentiment onindustry return with OLS the equation is

119877119894119905

= 1205720+ 1205721Sent119905+ 120576119905 (4)

Table 4 presents the estimates of coefficients and signif-icance levels for 23 industries regarding the effect of market


Table 4 Effect of sentiment on industry return

Industry Parameter estimate adj minus 119877

2 Industry Parameter estimate of adj minus 119877

2

Farming forestry animal husbandry and fishery 0010572lowastlowast 00494 Textile and garment 0012170lowastlowast 00615Extractive industry 0017801lowastlowast 01069 Light manufacturing 0011457lowastlowastlowast 00553Chemical industry 0013608lowastlowastlowast 01063 Biopharmaceuticals 0009759lowastlowast 00538Ferrous metal 0012803lowastlowastlowast 00626 Public utility 0010123lowastlowastlowast 00678Nonferrous industry 0018426lowastlowastlowast 00899 Transportation 0011796lowastlowastlowast 00878Construction materials 0014664lowastlowastlowast 00962 Real estate 0015494lowastlowastlowast 01034Mechanical installation 0014671lowastlowast 00970 Financial service 0010219lowastlowast 00533Electronics 0009823lowast 00378 Trade and business 0014061lowastlowastlowast 00997Transportation equipment 0016164lowastlowastlowast 01033 Catering and tourism 0008872lowast 00330Information equipment 0009669lowast 00397 Information service 0008983lowastlowastlowast 00487Household appliance 0013644lowastlowastlowast 00856 General industry 0008103 00252Food and beverage 0010993lowastlowastlowast 00684Notes lowastlowastlowast lowastlowast and lowast denote respectively significance at the significance level of 1 5 and 10

Table 5 Effect of investor sentiments of the current period and one period lagged

Industry Parameter estimate1205731

Parameter estimate1205732



Farming forestryanimal husbandry andfishery

0037385lowastlowast minus0028318lowast Textile and garment 0048461lowastlowastlowast minus0038231lowastlowast

Extractive industry 0056997lowastlowastlowast minus0041332lowastlowast Light manufacturing 0040493lowastlowast minus0030612lowast

Chemical industry 0044125lowastlowastlowast minus0032238lowastlowast Biopharmaceuticals 0030392lowastlowast minus0021772Ferrous metal 0053247lowastlowastlowast minus0042409lowastlowast Public utility 0041732lowastlowastlowast minus0033375lowastlowastlowast

Nonferrous metal 0065028lowastlowastlowast minus0049041lowastlowast Transportation 0046340lowastlowastlowast minus0036269lowastlowastlowast

Construction material 0061296lowastlowastlowast minus0049067lowastlowastlowast Real estate 0042135lowastlowastlowast minus0027891lowast

Mechanical installation 0039774lowastlowastlowast minus0026484lowast Financial service 0042135lowastlowast minus0010572lowastlowast

Electronics 0037814lowastlowast minus0029529lowast Business and trade 0030454lowastlowast minus0021355Transportationequipment 0057564lowastlowastlowast minus0043570lowastlowastlowast Catering and tourism 0041507lowastlowastlowast minus0028868lowastlowast

Information equipment 0028910lowast minus0020259 Information service 0023528lowast minus0015257Household appliances 0038257lowastlowast minus0026050lowast Integration 0004006 00004154Food and beverage 0038429lowastlowastlowast minus0028924lowastlowast


sentiment on the returns of specific industries It shows thatmarket sentiment is significantly and positively correlatedwith the current return of a specific industryMore optimisticmarket sentiment of the current period leads to a largernumber of stock demand and in turn greater stock returnamongwhich the greatest effect of investor sentiment appearsin nonferrous material industry with the parameter estimateof 0018426 This may be probably attributed to industriesclosely connected to financial industry of nonferrous materi-als when the financial industry of nonferrous materials goeswell the stock trading of nonferrous materials will increasegreatly when the financial industry of nonferrous materialsgoes bad the demand for nonferrous material stock becomesmuch smaller And at the same time overinvestment causesserious excess of production capacity The impact of marketsentiment on the financial industry of nonferrous materialscouples with the impact on the industry of nonferrousmaterial leading to low expectations with the consequencesof sharper decrease in nonferrous material stock trading

Therefore this may be the reason for the relatively greatereffect of investor sentiment on the nonferrousmetal industry

32 Investor Sentiment Effect of Different Periods on theReturns of Specific Industries In the study of investor senti-ment effect on the returns of specific industries we shouldconsider that investor sentiment at different period willhave different impacts on industry return because peoplersquosinherent mind sets and habits often lag behind the change ineconomic decisionsThronging autocorrelation test it can befound that the level of investor sentiment is one-period lagso we introduce the market sentiment level of the one periodlagged in (4) to verify the effect of sentiment levels of differentperiods on the returns of specific industries

119877119894119905

= 1205730+ 1205731Sent119905+ 1205732Sent119905minus1

+ 120576119905 (5)

The results in Table 5 show that the goodness of fit hasbeen appreciably improved after investor sentiment at lag


one is introduced into the regression the coefficients ofinvestor sentiment for the current period are all significantlypositive while those for the one period lagged are all negativewith six coefficients insignificant This fact indicates that thestock return is positively correlated with investor sentimentat the current period and negatively correlated with investorsentiment at one-period lag Meanwhile the phenomenonthat coefficients for investor sentiment at the current periodare all greater than those coefficients for lag one implies thatthere exists price overcorrection for lag one in the Chinesestock market

33 The Effect of Different States Investor Sentiment onIndustry Returns In order to clearly understand the effectof different investor sentiment levels on the industry returnsinvestor sentiment is divided into two kinds optimism andpessimismThe division of optimism and pessimism is wheninvestor sentiment index is greater than zero it is defined asthe optimistic month while it is defined as the pessimisticmonth if it is smaller than zero The statistical results areshown in Table 6

Table 6 shows that the industry return of the optimisticperiod is greater than that of the pessimistic period In thesampling period there are 57 months when investors areoptimistic of which the market average returns are 0395745and there are 40 months when investors are pessimistic ofwhich the average market income is minus036907 The differencebetween the two is 0764818

For the effect of optimistic and pessimistic investorsentiment on industry return with OLS the equation is

119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905

+ 119888 (2) pessimisticSent119905+ 120576119905

(6)

From the results shown in Table 7 we can see thatwhen investor sentiment index value is positive optimisticinvestor sentiment has a positive effect on the returns of mostindustries because fundamentals continue to be better andinvestorsrsquo investment and speculative motives are strength-ened to cause the market to rise all the way However wheninvestor sentiment index value is negative the effect of thepessimistic investor sentiment on the stock returns is notsignificant because investors will weaken their motivationto participate in the market when the market sentiment ispessimistic and they will be wary of entering the marketand even hold the stocks refusing to sell them because ofthe heavy loss they have already suffered To some extentthis also prevents the stock price from falling sharply Atthe same time the proportion of the irrational investors willgo down in this period and rational investors will occupy adominant position Therefore the effect that the sentimentof the pessimistic investors impacts on industry returns willbecome insignificant

34 Studies on Effect of Investor Sentiment on Industry ReturnBased onMarkov Regime Switching With the development ofthe financial markets and adjustment of macroeconomic pol-icy the market state has changed which changes coefficients

Table 6 Statistics of market returns for optimistic and pessimisticperiods

Sent gt0 Sent lt0 Total sampling periodMean 0395745 minus036907 0080357Median 0 0 0052068Standard deviation 1843508 1055102 2140861Skewness 0142774 minus1819949 minus0048180Kurtosis 4541919 1284935 3416804Observations 57 40 97

of estimated industry returns within the model accordinglyTo capture this kind of change the paper employs theMarkovregime switching model

After adopting the Markov regime switching model thepaper compares the monthly stock index of the currentperiod with the indexes three months before and after thecurrent period in order to further verify the bearish or thebullish state If the index of the current period is at the highestposition itmeans a peak and it is called the bullmarket if it isat the lowest position it means a trough and it is consideredto be the bear market

341 General Model In order to investigate the effect ofinvestor sentiment on industry returns this paper proposesthe following regression model

119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)

where 119877119894119905is the industry return at time 119905 and Sent

119905denotes

the investor sentiment

342 Markov Regime Switching Models This paper employsthe 119864-119872 algorithm proposed by Hamilton There is119872 time-varying regression equation between the returns of industry119894 and investor sentiment and it represents effects of investorsentiment on industry returns in different states where statevariable 119878

119905denotes homogenous unobservable stochastic

variable of 119905 and has the first-order Markov process in thestate space its transitionmatrix119875 = (119901

119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872

119895=1119901119894119895= 1 for any 119905 the current state is only

correlated with the state of one-period lag while other paststates do not have any effect The stochastic state variable isset to be one or two and the switching of investor sentimentis not a continuous change At this time (8) is

119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)


Table 7 Effects of optimistic and pessimistic sentiment on industry returns

Industry Parameterestimate 119888(1)

Parameterestimate 119888(2) Industry Parameter

estimate 119888(1)Parameter

estimate 119888(2)Farming forestry animalhusbandry and fishery 0019735 0001824 Textile and garment 0037789lowastlowast minus0012290

Extractive industry 0050252lowastlowastlowast minus0013182 Light manufacturing 0027157lowast minus0003533Chemical industry 0034506lowastlowastlowast minus0006345 Biopharmaceuticals 0019993 0000000Ferrous metal 0030332lowastlowast minus0003394 Public utility 0027694lowastlowast minus0006654Construction material 0033261lowastlowast minus0003092 Real estate 0039997lowastlowastlowast minus0007899Mechanical equipment 0029462lowastlowast minus0000549 Financial service 0031956lowastlowastlowast minus0010535Electronics 0023487 minus0003223 Business and trade 0033691lowastlowast minus0004681

Transportation equipment 0038812lowastlowast minus0005461 Catering andtourism 0024919lowast minus0006449

Information equipment 0016593 0003059 Information service 0021967lowast minus0003415Household appliances 0027274lowast 0000631 Integration 0018913 minus0002284Food and beverage 0028954lowastlowastlowast minus0006273Notes lowastlowastlowast lowastlowast and lowast denote respectively significance at the significance level of 1 5 and 10

Vector denotes the state of the system (industry subscriptsomitted)

120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)

Then the parameters to be estimated in (6) can be expressedin (9)

119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)

The conditional density in different states is

120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)

where 119868119905minus1

denotes the information set at time 119905 minus 1 and 120579 isthe parameter set of the parameters to be estimated that is1198861sdot sdot sdot 119886119872 1198871sdot sdot sdot 119887119872 and 120590

2

1sdot sdot sdot 120590

2

119872 and of the components of

the transitionmatrix that is 11990111

sdot sdot sdot 119901119872119872

and in the state 120577119905minus1

with the information set at time 119905minus1 that is 119868119905minus1

themarginaldensity function of 119903

119905follows a mixed normal distribution

with its probability density

119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)

where otimes denotes the multiplication of two vectors and 1represents (119872 times 1) vectors with all the component to be1 Formula (7) shows that there are 119872 industries and theimpacts of investor sentiment in different states on themarket returns of the119872 industries are different The optimalinference and prediction of 120585

119905|119905based on the information

set at time 119905 minus 1 can be obtained from iteration of (14) Atlast all the parameter can be estimated through maximizingthe likelihood function Probabilities obtained from all theobservations are called smoothed probabilities The Markovregime switching models can separate the data automaticallyto identify different state intervals and thus avoid the biascaused by subjective segmentation

120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)

343 Empirical Analysis Comparing the AIC value or theBIC value we can find that the two-state Markov process ismore useful Moreover the goodness of fit has been greatly


improved when adopting the Markov process We estimatethe parameters of (7) on R software which are shown inTable 8

At first comparing the stock index of an industry inthe current period with those indexes three months beforeand after the current period we can find that the split sharestructure reform started in May 2005 the issuing of a largenumber of open-end funds and the expectation of RMBappreciation led to excess liquidity in the securities marketand return indexes of all industries went up all the way Ifwe select the data for all industries around January 2007we can see that the data at this sentiment level are relativelyhighs (which makes a crest) that is all the industries are in abull market So all industries are at state onemdasha bull marketBut starting from 2007 with the influence of a series of badnews such as the soaring of inflation the suspension of theissuing of funds and the US subprime crises the Chinesestock market fell into a long bearish period and all indexesfor various industries plummeted We choose the data for allindustries around January 2010 and see that the indexes atthis sentiment level are at a relatively low level whichmakes atrough We can believe that all the industries are in a bearishmarket that is for all the industries the state is two a bearishmarket

Secondly with the state being set we test whether theswitching of the state significantly affects the coefficientsfor investor sentiment index In Table 8 we can see thatthe effects of investor sentiment on the stock returns ofindustries are quite different in the bull market and in thebear market For agriculture forestry animal husbandry andfishery mining ferrous metals textiles and services andbusiness and trade sectors effects of investor sentiment onstock returns of these industries are significant in the bullmarket while in the case of a bear market effects are notsignificant Animal husbandry and fishery and extractiveindustries belong to the foundational industries in nationaleconomies and are closely related to economic trends Whenthe market is bullish it will promote the development ofthose industries and investors will have greater interest instocks of these industries and choose to buy more of thesestocks for an optimal investment portfolio therefore theeffect of investor sentiment at this state is significant on theseindustries When the market is bearish investors may chooseto avoid this type of stocks and effect of investor sentimenton stock returns of these foundational industries becomesless significant For chemical industry nonferrous metalsbuilding materials and construction biopharmaceuticalsfinancial service and general industries the effect of investorsentiment on returns of these industries is not significantwhen it is a bull market while in the case of a bear marketthe effects of investor sentiment on the stock are significantThis may be because nonferrous metals and petrochemicalcategory belong to resource-based industry and investorswillincrease the investment in resources stocks to avoid riskswhich makes these stocks more resistant to risks Thereforethe effect of investor sentiment on these stocks is moresignificant in a bear market while in a bull market it becomesinsignificant For industries such as mechanical equipmentelectronics transportation equipment household appliances

food and beverage light manufacturing public utilitiestransportation real estate catering and tourism and infor-mation services the effect of investor sentiment on returnsof the industry is significant whether it is in a bull marketor in a bear market Investor sentiment to the stocks ofthese industries is generally stable This may be due tothe fact that industries of household appliances food andbeverage and other consumer goods are generally stable andthus will not change dramatically with economic conditionsFor information equipment industry whether it is in a bullmarket or a bear market the effect of investor sentiment isnot significant because information equipment industry is ahigh-tech industry Chinarsquos information industry is relativelybackward and cannot play a role in leading the stocks ofthe information industry Consequently the effect of investorsentiment on the return of the information equipment indus-try in China is relatively small either in a bull market or in abear market

At last the effect of investor sentiment on returns ofstocks of different industries is different in duration Foragriculture forestry animal husbandry and fishery min-ing ferrous metals textiles and services and commercialtrade industries the expected duration of the effect in stateone is 286 641 481 581 and 362 months respectivelyFor industries such as processing of agricultural productschemicals nonferrous metals building materials construc-tion biopharmaceuticals financial services and generalindustry the expected durations are 334 351 1302 1527456 3690 and 505 months respectively for industriessuch as mechanical equipment electronics transportationequipment household appliances food and beverage lightmanufacturing public utilities transportation real estatecatering and tourism and information services industry theexpected duration of the effect in state one is 1017 25062725 575 388 3344 2193 2681 524 3058 and 2967months respectively the expected duration of the effect instate 2 is 256 3058 3472 819 137 2732 6329 2227 19692618 and 2933 months respectively

In short each industry has its own characteristics Forresource-based industries such as nonferrous metals andpetrochemicals the effect of investor sentiment on stockreturns of these industries is relatively significant in a bearishmarket condition while the effect is insignificant when thestock market is bullish As for household appliances foodand beverage and other consumer goods industries the effectof investor sentiment on stock returns of these industriesis generally stable There is no significant effect of investorsentiment on stock returns of the information equipmentindustry whether it is in a bull market or bear market

344 Smoothed Probability Analysis In order to furtherunderstand the duration of each state and the maximumprobability for which state may appear in each period we canfurther investigate the effect of investor sentiment on eachindustry through the smoothed probability in Figure 2 Hereit is regarded as the bull market when Pr(119904

119905= 1 | 119868

119905minus1=

119894) gt 05 and as the bear market when Pr(119904119905= 2 | 119868

119905minus1=

119894) gt 05 Due to space limitations this paper only presents


Table 8 Effects of investor sentiment on industry returns based on Markov regime switching

IndustryFarming forestryanimal husbandry

and fishery

Extractiveindustry

Chemicalindustry Ferrous metal Nonferrous

metalConstructionmaterials

1198861

00704lowastlowastlowast 00677lowastlowastlowast minus00436 00737lowastlowastlowast minus00701lowast minus00584lowast

1198871

00324lowastlowastlowast 00372lowastlowastlowast 00009 00372lowastlowastlowast minus00255 00263Root MSE 00458 00499 00699 00638 01430 00889119877 Square 07065 07299 00006 06059 00751 011761198862

minus00213 minus00335 00494lowastlowast minus00455lowastlowastlowast 00360lowastlowastlowast 00679lowastlowastlowast

1198872

minus00003 00081 00247lowastlowastlowast 00000 00282lowastlowastlowast 00373lowastlowastlowast

Root MSE 00921 01096 00516 00818 00822 00589119877 Square 08693 001704 05171 04835 03572 05914AIC minus1902188 minus1780989 minus2224067 1806269 minus1467789 minus202075BIC minus1616211 minus1495012 minus1938090 minus1520292 minus1181812 minus1734773LL 991094 930495 1152033 943135 773895 1050375P11 06506 08439 07096 06944 07721 09454P12 01876 01089 02848 02075 00768 00655P21 03494 01561 02904 03056 02279 00546P22 08124 08911 07152 07925 09232 09345

Industry Mechanicalequipment Electronics Transportation

equipmentInformationequipment

Householdappliances

Catering andtourism

1198861

minus00251 lowastlowast 00523lowastlowastlowast 00594lowastlowastlowast minus00649lowastlowast 00734lowastlowastlowast 001201198871

00114lowastlowast 00273lowastlowastlowast 00324lowastlowastlowast 00234 00245lowastlowastlowast 00119lowastlowast

Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862

01029lowastlowastlowast minus00799lowastlowastlowast minus01003lowastlowastlowast 00487 minus00472lowastlowast 00169lowastlowastlowast

1198872

00229lowastlowastlowast 00310lowastlowast 00513lowastlowastlowast 00269 00181lowastlowast 00090lowastlowastlowast

Root MSE 00344 01047 00959 00662 00788 00235119877 Square 06622 01226 03003 03695 01683 04361AIC minus1937313 minus1780449 minus1982534 minus1860705 minus1976915 minus2098202BIC minus1651336 minus1494472 minus1696557 minus1574728 minus1690938 minus1812225LL 1008657 930225 1031267 970352 1028457 1089101P11 09017 09601 09633 09658 08262 07425P12 03909 00327 00288 00389 01221 07326P21 00983 00399 00367 00342 01738 02575P22 06091 09673 09712 09611 08779 02674

Industry Textile andgarment

Lightmanufacturing Pharmaceuticals Public utilities Transportation Real estate

1198861

00834lowastlowastlowast minus00876lowastlowastlowast -00088 minus00552 minus00742lowastlowastlowast minus01506lowastlowastlowast

1198871

00375lowastlowastlowast 00361lowastlowast 00049 00390lowastlowast 00330lowastlowastlowast 00567lowastlowastlowast

Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862

minus00317lowastlowast 00517lowastlowastlowast 00758lowastlowastlowast minus00013 0039lowastlowastlowast 00362lowastlowastlowast

1198872

00039 00285lowastlowastlowast 00302lowastlowastlowast 00053lowast 00260lowastlowastlowast 00205lowastlowastlowast

Root MSE 00849 00617 00514 00498 00496 00692119877 Square 00067 04282 06222 003928 04871 02897AIC minus1926297 minus1962553 minus2089941 minus245056 minus2382588 minus2064154BIC minus1640321 minus1676577 minus1803964 minus2164583 minus2096611 minus1778177LL 1003149 1021277 1084970 1265280 1231294 1072077


Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492

Industry Financial service Business andtrade

Catering andtourism

Informationservice General

1198861

minus00014 00563lowastlowastlowast 00388lowastlowastlowast minus00437 minus002521198871

00040 00281lowastlowastlowast 00168lowastlowastlowast 00305lowastlowast minus00005Root MSE 00496 00580 00689 01078 00926119877 Square 00196 05279 01992 01329 000011198862

minus00483lowast minus00338 minus00820lowastlowast 00132 00790lowastlowastlowast

1198872

00380lowastlowast 00038 00333lowast 00085lowastlowast 00401lowastlowastlowast

Root MSE 01141 00779 01169 00540 00682119877 Square 01492 000874 01153 008257 05604AIC minus2183481 minus2048813 minus188721 minus2217585 minus175087BIC minus1897504 minus1762837 minus1601233 minus1931609 minus1464893LL 1131741 1064407 9836051 1148793 9154349P11 09797 07239 09673 09663 09142P12 00271 02086 00382 00341 01980P21 00203 02761 00327 00337 00858P22 09729 07914 09618 09659 08020Notes lowastlowastlowast lowastlowast and lowast denote respectively significance at the significance level of 1 5 and 10

0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)

Figure 2 Smoothed probability of animal husbandry and fisheryindustry

the smoothed probability plots of the animal husbandry andfishery industry

4 Conclusion

This paper constructs a proxy variable for investor sentimentto examine the relationship between investor sentimentand the return of a specific industry using the PrincipalComponent Analysis and finds that investor sentiment ispositively correlated with the current period industry returnand negatively correlated with that for one period lagged andinvestor sentiment coefficients for the current level are greater

than coefficients for one period lagged which demonstratesthere exists a one-period price overcorrection in Chinarsquosstock market according to a standard investor sentiment isclassified into two kinds the optimistic and the pessimisticand optimism shows positive effects on stock returns onmostindustrieswhile the pessimistic yields no significant effects onthe majority of industriesrsquo stocks

In this paper we establish a two-state Markov model toidentify the shifting between the bull market and the bearmarket which helps to study the effect of investor sentimenton the industry returns in the bear market and in the bullmarket It finds that the animal husbandry and fishery indus-try and the extractive industry belong to the foundationalindustry of the national economy and are closely relatedto economic trends When the stock market is bullish themarket condition will promote the development of thesefoundational industries When the stock market is bearishinvestors may choose to avoid stocks of these industries andthus the effect of investor sentiment on stock returns ofthese foundational industries will become less significantFor resource-based industries such as nonferrous metals andpetrochemicals the effect of investor sentiment on stockreturns of these industries is relatively significant in a bearishmarket condition while the effect is insignificant when thestock market is bullish As for household appliances foodand beverage and other consumer goods industries the effectof investor sentiment on stock returns of these industriesis generally stable There is no significant effect of investorsentiment on stock returns of the information equipmentindustry whether it is in a bull market or bear market Each


industry has its own characteristics To construct investmentportfolios with a consideration of the differences in the effectof investor sentiment on returns of different industries indifferent market states is of important reference value tolarge institutional investors in allocating their funds amongdifferent industries in the securities market

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was jointly supported by the National NaturalScience Foundation of China under Grants nos 1110105370921001 and 71171024 the Key Project of Chinese Ministryof Education under Grant no 211118 the Excellent YouthFoundation of Educational Committee of Hunan Provincialno 10B002 the Hunan Provincial NSF under Grant no11JJ1001 and the Scientific Research Funds of Hunan Provin-cial Science and Technology Department of China underGrant no 2013SK3143

References

[1] J Bradford De Long A Shleifer L H Summers and RJ Waldmann ldquoPositive feedback investment strategies anddestabilizing rational speculationrdquo Journal of Finance no 45pp 379ndash396 1990

[2] W Y Lee C X Jiang and D C Indro ldquoStock market volatilityexcess returns and the role of investor sentimentrdquo Journal ofBanking and Finance vol 26 no 12 pp 2277ndash2299 2002

[3] G W Brown and M T Cliff ldquoInvestor sentiment and assetvaluationrdquo Journal of Business vol 78 no 2 pp 405ndash440 2005

[4] M Baker and J Wurgler ldquoInvestor sentiment and the cross-section of stock returnsrdquo Journal of Finance vol 61 no 4 pp1645ndash1680 2006

[5] M Lemmon and E Portniaguina ldquoConsumer confidence andasset prices some empirical evidencerdquo Review of FinancialStudies vol 19 pp 1499ndash1529 2004

[6] R F Stambaugh J Yu and Y Yuan ldquoThe short of it investorsentiment and anomaliesrdquo Journal of Financial Economics vol104 no 2 pp 288ndash302 2012

[7] A Ben-Rephael S Kandel and A Wohl ldquoMeasuring investorsentiment with mutual fund flowsrdquo Journal of Financial Eco-nomics vol 104 no 2 pp 363ndash382 2012

[8] M Baker JWurgler andY Yuan ldquoGlobal local and contagiousinvestor sentimentrdquo Journal of Financial Economics vol 104 no2 pp 272ndash287 2012

[9] MWang and J J Sun ldquoStock market returns volatility and roleof investor sentiment in Chinardquo Economic Research Journal no10 pp 75ndash83 2004

[10] X Huang ldquoInvestor sentiment on the expected return andvolatility the influence of difference of empirical research basedon the industryrdquo 2012

[11] Q Zhang and S Yang ldquoNoise trading investor sentimentvolatility and stock returnsrdquo System Engineering Theory andPractice vol 29 no 3 pp 40ndash47 2009

[12] L Chi and X Zhuang ldquoA study on the relationship betweeninvestor sentiment and the stockmarket returns in China-basedon panel data modelrdquo Management Review no 6 pp 41ndash482011

[13] X Lu and K Lai ldquoRelationship between stock indices andinvestorsrsquo sentiment index in Chinese financial marketrdquo SystemEngineeringTheory and Practice vol 32 no 3 pp 621ndash629 2012

[14] J D Hamilton Analysis of Time Series China Social SciencePress Beijing China 1999

[15] M Lanne H Lutkepohl and K Maciejowska ldquoStructuralvector autoregressions with Markov switchingrdquo Journal ofEconomic Dynamics and Control vol 34 no 2 pp 121ndash131 2010

[16] R E A Farmer D F Waggoner and T Zha ldquoMinimal statevariable solutions to Markov-switching rational expectationsmodelsrdquo Journal of Economic Dynamics and Control vol 35 no12 pp 2153ndash2166 2011

[17] F Chen F X Diebold and F Schorfheide ldquoAMarkov-switchingmultifractal inter-trade duration model with application to USequitiesrdquo Journal of Econometrics vol 177 no 2 pp 320ndash3422014

[18] C Lee A Shleifer and R Thaler ldquoInvestor sentiment and theclosed-end fund puzzlerdquo Journal of Finance vol 46 no 1 pp75ndash109 1991

[19] Y Wu and L Y Han ldquoImperfect rationality sentiment andclosed-end-fund puzzlerdquoEconomic Research Journal vol 42 no3 pp 117ndash129 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


and local sentiments are contrarian predictors of the timeseries of cross-sectional returns within markets Wang andSun [9] showed that investor sentiment does not only affectthe returns of Shanghai and Shenzhen stockmarkets but alsoreversely corrects return fluctuations of these two marketsto a large extent Study by Huang [10] finds that there is adistinct cross-sectional effect between the investor sentimentindex and the expected return of the market and the effectis reflected in return indices for different industries with thelargest effect on the information industry and the least effecton the transportation industry

Some scholars classify investor sentiment as the opti-mistic state and the pessimistic state in order to examinethe effect of investor sentiment on the return of a specificindustry For example Zhang and Yang [11] adopt GARCH-M Model to prove that institutional investor sentiment hasa great effect on stock returns and sentiment rise has agreater effect on stock returns than sentiment decline Chiand Zhuang [12] demonstrated investor sentiment affectsstock returns significantly and the effect of optimistic sen-timent is greater than that of pessimistic sentiment Besidesextreme sentiment has a special predictive power in the stockmarket Lu and Lai [13] showed that investor sentiment hasa significant effect on the Shanghai composite index Whenthe market is in a rising stage investor sentiment is moreoptimistic and more investors enter the market when themarket is in a declining stage investor sentiment is relativelypessimistic and investors will wait to enter the market

The state of the financial market (bearish or bullish)changes accordingly with the continuous change in the finan-cial market and the adjustment of macroeconomic policywhich will lead to corresponding changes of the coefficientsfor the econometric model for the return of an industryOne of the models to capture this kind of coefficient changeis the Markov switching regime model with state changeHamilton [14] introduced for the first time theMarkov regimeswitching model into a variable structure model and studiedthe effect of the cyclic changes of the US economy on theactual output from 1953 to 1984 Later a large number ofresearchers adopted the Markov regime switching model tocharacterize endogenic structural changes such as Lanne etal [15] Farmer et al [16] and Chen et al [17] This paperattempts to verify the bull and bear market using the two-stateMarkov regime switchingmodel On this basis it furtherexamines the changes in the effect of investor sentiment onreturns of different industries in different market states

Previous studies showed that investor sentiment signifi-cantly affects stock returns Which kinds of industryrsquos stocksare more easily affected by investor sentiment Are thereany differences between their effects of the optimistic andthe pessimistic states on returns of an industry What is thedifference between the effects of investor sentiment on thereturn of an industry at different market states Aiming atthese questions this paper will conduct close explorationsAnd my paperrsquos main contribution is to set a two-stateMarkov regime switching model to find that sentiment hasdifferent effect on different industries returns on differentstates of marketThe remaining part of this paper is arrangedas follows the second part is for the index construction of

investor sentiment the third part is an empirical study andthe fourth part is the conclusion

2 Proxy Index Construction ofInvestor Sentiment

21 The Selecting of Proxy Indicator of Investor SentimentAt present there are two measures for investor sentimentmdashthe direct approach and the indirect approach The directapproach is rather subjective and can get only a portionof investor feedbacks Therefore most investor sentimentmeasurements adopt the index in Baker and Wurgler study[4] which selects these six variablesmdashthe average closed-endfund discount (CEFD) NYSE share turnover (TURN) thenumber on IPOs (NIPO) average first-day returns on IPOs(RIPO) the equity share in new issues and the dividendpremium to form an investor sentiment variable based onthe Principal Component Analysis Considering the charac-teristics of the Chinese stock market and the availability ofdata this paper selects CEFD NIPO RNIPO the numberof new investor accounts for A shares (NIA) and Shanghaishare turnover (TURN) to form a proxy variable for investorsentiment based on the Principal Component Analysis Thesamples are monthly data from the Resset database duringJanuary 2005 to January 2013 (httpwwwressetcn)

(1) CEFD CEFD is the ratio of the difference between thenet asset value (NAV) and unit price of the closed-end fundto NAV Lee et al [18] find that investor sentiment canbe measured by CEFD and it also gives a comprehensiveexplanation to the closed-end fund discount puzzle Wuand Han [19] show that CEFD can be a proxy variable forinvestor sentimentWhen there is a high CEFD stockmarketinvestors lack confidence and their sentiment is low

The calculation formula is

CEFD119905=

sum

119899

119894=1((119875119894119905minusNAV

119894119905) (NAV

119894119905))

119899

(1)

where119875119894119905is the closing price of fund 119894 inmonth 119905 NAV

119894119905is the

last NAV published in month 119905 and 119899 represents the numberof the selected funds

(2) NIPO Initial public offering (IPO) is the process forthe enterprise to firstly issue stocks to investors in the stockexchange for the first time to raise funds for its developmentWhen the market sentiment runs high the stock price willgrow and the pace of IPOs will speed up leading to moreIPOs during such high market sentiment period On thecontrary when the market is in low sentiment the stockmarket will slow down or even suspend the issuing of newstocks Empirical evidence presented by Baker and Wurgler[4] finds that the number of IPOs (NIPO) is a good proxyvariable for investor sentiment

(3) RIPO RIPO denotes the return on the IPO in the firsttrading day namely the percentage of the closing price to theoffering price When the market sentiment is high investorswill have a greater interest in the new stock thus resultingin higher return on the IPO (RIPO) Otherwise low investor











CEFD119905

NIPO119905

RIPO119905

TURN119905

NIA119905

CEFD119905minus1

NIPO119905minus1

RIPO119905minus1

TURN119905minus1

NIA119905minus1

SentRAW119905

0761 minus0700 0565 0745 0378 0766 minus0723 0559 0740 0333







SentRAW119905

= 0372646CEFD119905minus 0342926NIPO

119905

+ 0276802RIPO119905+ 0364866TURN

119905

+ 0185272NIA119905+ 0375499CEFD

119905minus1


+ 0273913RIPO119905minus1

+ 0362383TURN119905minus1

+ 0163127NIA119905minus1

(2)





119905minus1 NIPO

119905minus1 RIPO

119905 TURN

119905



119905

Sent119905= 0477612CEFD


119905minus1

+ 0436559RIPO119905+ 0522063TURN

119905

+ 0289835NIA119905

(3)




























minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

Jan-05

Jul-0

5

Jan-06

Jul-0

6

Jan-07

Jul-0

7

Jan-08

Jul-0

8

Jan-09

Jul-0

9

Jan-10

Jul-1

0

Jan-11

Jul-1

1

Jan-12

Jul-1

2

Jan-13



3 Empirical Study



=

ln119901119894119905

minus ln119901119894119905minus1





119877119894119905

= 1205720+ 1205721Sent119905+ 120576119905 (4)






2




















119877119894119905

= 1205730+ 1205731Sent119905+ 1205732Sent119905minus1

+ 120576119905 (5)







119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905


(6)








119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)


119905denotes





119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872



119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)











120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















CEFD119905

NIPO119905

RIPO119905

TURN119905

NIA119905

CEFD119905minus1

NIPO119905minus1

RIPO119905minus1

TURN119905minus1

NIA119905minus1

SentRAW119905

0761 minus0700 0565 0745 0378 0766 minus0723 0559 0740 0333







SentRAW119905

= 0372646CEFD119905minus 0342926NIPO

119905

+ 0276802RIPO119905+ 0364866TURN

119905

+ 0185272NIA119905+ 0375499CEFD

119905minus1


+ 0273913RIPO119905minus1

+ 0362383TURN119905minus1

+ 0163127NIA119905minus1

(2)





119905minus1 NIPO

119905minus1 RIPO

119905 TURN

119905



119905

Sent119905= 0477612CEFD


119905minus1

+ 0436559RIPO119905+ 0522063TURN

119905

+ 0289835NIA119905

(3)




























minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

Jan-05

Jul-0

5

Jan-06

Jul-0

6

Jan-07

Jul-0

7

Jan-08

Jul-0

8

Jan-09

Jul-0

9

Jan-10

Jul-1

0

Jan-11

Jul-1

1

Jan-12

Jul-1

2

Jan-13



3 Empirical Study



=

ln119901119894119905

minus ln119901119894119905minus1





119877119894119905

= 1205720+ 1205721Sent119905+ 120576119905 (4)






2




















119877119894119905

= 1205730+ 1205731Sent119905+ 1205732Sent119905minus1

+ 120576119905 (5)







119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905


(6)








119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)


119905denotes





119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872



119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)











120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



































minus4

minus3

minus2

minus1

0

1

2

3

4

5

6

Jan-05

Jul-0

5

Jan-06

Jul-0

6

Jan-07

Jul-0

7

Jan-08

Jul-0

8

Jan-09

Jul-0

9

Jan-10

Jul-1

0

Jan-11

Jul-1

1

Jan-12

Jul-1

2

Jan-13



3 Empirical Study



=

ln119901119894119905

minus ln119901119894119905minus1





119877119894119905

= 1205720+ 1205721Sent119905+ 120576119905 (4)






2




















119877119894119905

= 1205730+ 1205731Sent119905+ 1205732Sent119905minus1

+ 120576119905 (5)







119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905


(6)








119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)


119905denotes





119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872



119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)











120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













2




















119877119894119905

= 1205730+ 1205731Sent119905+ 1205732Sent119905minus1

+ 120576119905 (5)







119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905


(6)








119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)


119905denotes





119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872



119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)











120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119877119894119905

= 119888 (0) + 119888 (1) optimisticSent119905


(6)








119877119894119905= 119886119894+ 119887119894times Sent

119905+ 120576119894119905 (7)


119905denotes





119894119895) where119901

119894119895= Pr(119904

119905=

119895 | 119904119905= 119894) and sum

119872



119877119894119905= 119886119894+ 119887119894times sent + 120576

119894119905

120576119894119905sim (0 120590

2

119894119904119905)

119901119894119895= Pr (119904

119905= 119895 | 119904

119905= 119894)

119872

sum

119895=1

119901119894119895= 1

(8)











120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















120585119905=

[

[

[

[

[

[

[

[

119868 (119904119905= 1)

119868 (119904119905= 119895)

119868 (119904119905= 119898)

]

]

]

]

]

]

]

]

(9)

where

119868 (119904119905= 1) =

1 if 119904119905= 119895

0 else(10)


119886119904119905= [1198861 119886

119872] times 120585119905

119887119904119905= [1198871 119887

119872] times 120585119905

(11)


120578119905=

119891(119903119905| 119878119905= 1 119868119905minus1

120579)

=

1

radic2120587120590

2

1

minus(119903119905minus 1198861119905

minus 1198871119905

times Sent119905)

2

2120590

2

1

119891 (119903119905| 119878119905= 2 119868119905minus1

120579)

=

1

radic2120587120590

2

2

minus(119903119905minus 1198862119905

minus 1198872119905

times Sent119905)

2

2120590

2

2

119891 (119903119905| 119878119905= 119872 119868

119905minus1 120579)

=

1

radic2120587120590

2

119872

minus(119903119905minus 119886119872119905

minus 119887119872119905

times Sent119905)

2

2120590

2

119872

(12)



2


2



sdot sdot sdot 119901119872119872






119891 (119903119905| 119877119905 120585119905minus1

119868119905minus1

120579)

=

119872

sum

119898=1

119891 (119903119905| 120585119905minus1

119877119905 119868119905minus1

120579)Pr (120585119905minus1

)

= 1

1015840(120578119905otimes 120585119905|119905minus1

)

(13)




120585119905|119905

=

120585119905|119905minus1

otimes 120578119905

1

1015840(120585119905|119905

otimes 120578119905)

120585119905|119905+1

= 119875 otimes 120585119905|119905

(14)










119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















119905= 1 | 119868

119905minus1=


119905minus1=





and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












and fishery

Extractiveindustry



1198861


1198871



1198872





Householdappliances

Catering andtourism

1198861



Residual 00814 00719 00639 01070 00576 00950119877 Square 00739 03362 04699 00705 04206 0057741198862


1198872





1198861


1198871


Root MSE 00593 01037 00800 01159 00813 00611119877 Square 06511 01545 001349 01976 01959 051451198862


1198872




Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table 8 Continued

P11 08276 09701 09177 09544 09627 08090P12 01068 00366 02194 00158 00449 00508P21 01724 00299 00823 00456 00373 01910P22 08932 09634 07806 09842 09551 09492


Catering andtourism


1198861




1198872



0 20 40 60 80 100

00

06

Regime 1

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(a)

0 20 40 60 80 100

00

06

Regime 2

Smoo

thed

prob

abilitie

s

Filtered

prob

abilitie

s

(b)



4 Conclusion








Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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