Forecasting model primer_v1

FORECASTING OF TATA STEEL SALES Primer on estimation model 11/30/2010 Vinod Krishnan

Table of Contents INTRODUCTION ..................................................................................................................................3

Methodology......................................................................................................................................3

Regression......................................................................................................................................3

ARIMA............................................................................................................................................3

PRELIMINARY ANALYSIS ......................................................................................................................4

ARIMA METHOD .................................................................................................................................5

Identification of the Model ..............................................................................................................5

Estimation & Verification of the Model ............................................................................................5

Derivation of Forecast .....................................................................................................................6

REGRESSION METHOD ........................................................................................................................8

CONCLUSION.................................................................................................................................... 11

APPENDIX ........................................................................................................................................ 12

APPENDIX - I ................................................................................................................................. 13

APPENDIX – II ............................................................................................................................... 14

APPENDIX – III .............................................................................................................................. 72

ARIMA(2,0,8)(0,0,0) ...................................................................................................................... 72

ERROR DIAGNOSTIC................................................................................................................... 74

ARIMA(5,1,13)(0,0,0) .................................................................................................................... 78


ARIMA(4,0,4)(0,1,0) ...................................................................................................................... 83


ARIMA(0,1,4)(0,4,0) ...................................................................................................................... 88


ARIMA(4,1,6)(0,1,0) ...................................................................................................................... 93


APPENDIX – IV .............................................................................................................................. 99

INTRODUCTION

Tata Steel formerly known as TISCO and Tata Iron and Steel Company Limited is the world's 7th largest

steel company, with an annual crude steel capacity of 31 million tons. It is the largest private sector steel

company in India in terms of domestic production. Ranked 258th on, it is based in, Jharkhand, India. It is

part of Tata Group of companies. Tata Steel is also India's second-largest and second-most profitable

company in private sector with consolidated revenues of 132,110 crore (US$ 29.99 billion) and net

profit of over 12,350 crore (US$ 2.8 billion) during the year ended March 31, 2008. Tata steel Company

in the 8th most valuable brand according to an annual survey conducted by Brand Finance and The

Economic Times in 2010.

This project is focused at forecasting the sales of TATA Steel. APPENDIX-I contains the consolidated data.

The forecast methodology used would be ARIMA and Regression.

Methodology

Regression In theory it is assumed that the Sales of Tat steel would be dependent on the following variables,

Price of Steel

Income data of India

Price of Cement

Price of Electricity

Interest rate data

Car sales (units)

Money Supply data

ARIMA The popular time series method known as ARIMA would be applied on Tata Steel Sales. The parameters

of ARIMA model would be found out through trial and error method by looking at the ACF

(Autocorrelation function) and PACF (Partial Autocorrelation function) significance.

2000 – 2010 quarterly data of all the variables have been extracted

2000-2008 data will be used for forecast model development

2008 – 2010 data will be used for testing and verification

2011-2012 will be forecasted using the appropriate model

http://en.wikipedia.org/wiki/Indian_rupee


PRELIMINARY ANALYSIS

Exhibit 1 shows the quarterly movement of all the variables in the past 10 years. It can be seen that the

yield and price data are suppressed in scale because of the magnanimity of the Money Supply data.

Hence the data has been normalized and the resulting graph is shown in Exhibit 2.

Exhibit 1: Consolidated quarterly progression of all variables

Exhibit 2: Normalized quarterly progression of all variables

A quick view shows that there seems to be a lead-lag relationship between Money Supply and price of

steel.

Also it can be seen that the sales data is fairly consistent throughout the years nevertheless there seems

to be an inverse relationship between price of steel and sales of steel. A positive relationship is seen

between car sales and Tata steel sales.

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cement index

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yields

car sales(units)

tatasales

ARIMA METHOD

The ARIMA model is obtained through the examination of auto correlation (AC) and partial auto

correlation (PAC) coefficients of various orders. The significance of these coefficients was tested through

the Q Statistic.

Identification of the Model

Exhibit 3 shows the different combinations of the sales data that was tried to develop the best ARIMA.

Trial No Difference (d) Seasonal Difference (s) Significant ACF Lags (q)

Significant PACF Lags (p)

1 0 0 8 2

2 1 0 13 5

3 0 1 4 4

4 0 4 4 0

5 1 2 4 0

6 1 3 4 0

7 1 1 6 4

Exhibit 3: The different trials used to identify the best model

The complete results obtained from SPSS executions are available in APPENDIX-II.

Estimation & Verification of the Model After multiple trial and error attempts, of the monthly data it was decided to run the following ARIMA

models and then check for diagnostics on the residuals to verify the model

Diagnostics of the residuals involves checking the significance of residuals’ AC and PAC coefficients.

Exhibit 4 shows the various ARIMA models that were executed in SPSS based on the ACF and PACF

results shown in Exhibit 3.

ARIMA Stationary R-SQUARED Significance of residuals

ARIMA(2,0,8)(0,0,0) 85% Stationary error

ARIMA(5,1,13)(0,0,0) 67.20% Non-stationary error





ARIMA(4,1,6)(0,1,0) 69.40% Stationary error Exhibit 4: Table showing the significant results of ARIMA model of Tata Steel Sales

Appendix-III shows the SPSS results obtained by execution of the ARIMA models shown in exhibit 4.

Derivation of Forecast

With 87% Stationary R-Squared and strong stationary residual count, ARIMA(2,0,8)(0,0,0) was chosen as

the best model.

After checking the earlier phase it was found that the following MA and AR values are significant,

AR = 1,2

MA=1,2,3,4,5,6,7,8

Because of the presence of significant MA this model becomes nonlinear in Parameters.

The equation would be:

Xt= .838*Xt-1 +.359*Zt-2 -.512*et-1 +.838*et-2 + .809*et-3 +.696*et-4+

.652*et-5 + 546* et-6 +.493*et-7+.387*et-8+.357*et-9

The ex-post forecast (between 2009 and 2010) is shown in Exhibit 5

Quarter Short-Date Actuals Forecasted Residual

1 Jun-09 5554.02 6159.35 -605.33

2 Sep-09 5629.85 6390.23 -760.38

3 Dec-09 6307.48 5845.63 461.85

4 Mar-10 7225.47 6042.92 1182.55

1 Jun-10 6471.27 5401.25 1070.02

2 Sep-10 7038.13 6251.31 786.82

Exhibit 5: Tata sales Quarterly ex-post forecast from 2009-2010.

Exhibit 6 shows the ex-ante forecast from ARIMA for 2011-2013 of Tata steel

Quarter Short-Date Forecasted 3 Dec-10 5592.53

4 Mar-11 5693

1 Jun-11 5622.42

2 Sep-11 5565.29

3 Dec-11 5509.27

4 Mar-12 5455.11

1 Jun-12 5402.71

2 Sep-12 5352.01

3 Dec-12 5302.96

4 Mar-13 5255.5

Exhibit 6: Tata sales Quarterly ex-ante forecast from 2011-2013

REGRESSION METHOD The next model used for forecast is regression. Based on the preliminary analysis and theory of

economics, it is hypothesized that,

Sales of Tata Steel

is inversely related to price of steel (ST)

Is directly related to sales of cars (CS)

Is directly related to money supply (M3)

Is inversely related to interest rate, long-term rate, (Y)

Is directly related to price of cement (CI)

Is directly related or price of electricity (EL)

The equation would be as following,

TS = b0 + b1*CI + b2*CS + b3*M3 – b4*Y – b5*ST + b6*EL

APPENDIX –IV shows the SPSS results of the regression.

The regression equation estimated is:

TS=-1936.427 + 2.450*CI + .010*CS + .002*M3 - 62.82*Y - 11.436*ST + 9.995*EL

As can be seen the model conforms to the economic theory hypothesized above.

Fitness of the Model:

R-SQUARED = 94.9%

Durbin Watson = 1.970

Exhibit 7 shows the VIF values of each parameter and of the overall model.

Variable VIF 1/VIF

EL 6.94 0.144191

CS 6.77 0.147785

ST 6.37 0.156883

CI 5.94 0.16849

M3 2.29 0.436125

Y 1.65 0.604865

Mean VIF 4.99 0.200400802 Exhibit 7: VIF values

The model is also homoscedastic. Exhibit 8 shows the variance of the residuals.

Exhibit 8: Shows that the residuals are insignificant and random.

This regression model is expected to be the best forecast of the Sales of TATA Steel. The model has been

diagnosed for the common regression assumptions,

Autocorrelation: DW of 1.97 is close to the required DW of 2

Multicollinearity: VIF of 4.99 is less than required 10

Homoscedasticity: as shows in exhibit 8 the residuals are homoscedastic and random.

And the model conforms to economic theory

Exhibit 9 shows the forecast obtained through ex-post forecast obtained through regression equation

Quarter Short-Date Actuals Forecasted Residual 1 Jun-09 5554.02 4887.629478 666.3905

2 Sep-09 5629.85 5292.812682 337.0373

3 Dec-09 6307.48 5490.476696 817.0033

4 Mar-10 7225.47 6548.756815 676.7132

1 Jun-10 6471.27 6355.713014 115.557

2 Sep-10 7038.13 6651.213221 386.9168

Exhibit 9: Tata sales Quarterly ex-post forecast from 2009-2010.

Exhibit 10 shows the ex-ante forecast from Regression for 2011-2013 of Tata steel

Quarter Short-Date Forecasted 3 Dec-10 6287.861387

4 Mar-11 7646.294791

1 Jun-11 7264.161005

2 Sep-11 7686.26784 3 Dec-11 7205.096263

4 Mar-12 8951.878836

1 Jun-12 8296.357874

2 Sep-12 8906.727713 3 Dec-12 7205.096263

4 Mar-13 8951.878836

Exhibit 10: Tata sales Quarterly ex-ante forecast from 2011-2013

CONCLUSION

After thorough analysis and execution of both Regression and ARIMA method to forecast sales pattern

of TATA Steel it has been found that the sales of the company is fairly predictable.

It is exhibited that Regression is a better and stronger forecasting technique as sales of the company is

extremely dependant on exogenous factors and doesn’t have a particular time -series pattern.

Some interesting finds are the lead-lag relationship between money supply and price of steel which

again affects the sales of TATA steel directly. Hence Money supply is a strong indicator of the sales of

Tata steel. Car sales are also a strong indicator of the sales.

Although all forecasts methods are subject errors, as per the current analysis it can be said that the Sales

of TATA steel would hopefully be close to 8000 Crores by the end of Mar 2013.


APPENDIX

APPENDIX – I

Quarter Mon-yy cement-index cement-prices steel-prices electricity M3 yields car sales(units) tatasales1 Jun-00 125.9 125.33 118.7333333 191.4 80,666.00 6.76 32077 1401.226087

2 Sep-00 128.7333333 132.17 117.8333333 195.8333333 21,512.00 7.08 34847 1666.318966

3 Dec-00 137.7333333 137.67 114.2666667 202.2666667 70,446.00 7.11 34649 1868.17

4 Mar-01 154.1 145.5 106.8666667 210.7 44,347.00 7.26 48782 2353.5

1 Jun-01 151.7 139 103.5 213.4 70,376.00 6.98 30207 1611.41

2 Sep-01 149.3 141.58 103.5 219.9333333 29,435.00 7.12 37856 1932.93

3 Dec-01 147 138.83 103.5 232.9666667 44,340.00 7.28 38316 1902.21

4 Mar-02 146.7666667 127.67 102.1333333 233 50,285.00 7.34 51960 2150.52

1 Jun-02 144.6333333 131.17 103.9666667 230.5 117,345.00 7.57 41580 1988.05

2 Sep-02 143.2333333 130.83 119.3 239.4 21,349.00 7.20 47142 2332.62

3 Dec-02 145.8333333 131.33 119.3 241 41,373.00 6.46 50209 2491.29

4 Mar-03 147.6 122.83 128.7 241 44,508.00 5.91 63937 2981.31

1 Jun-03 147.6 128.17 140.5666667 245.8 81,381.00 5.62 49211 2522.93

2 Sep-03 144.3 122.83 145.4 247.2333333 31,739.00 5.11 66850 2940.98

3 Dec-03 145.2666667 130 151.8333333 250.5666667 61,371.00 5.14 73237 2967

4 Mar-04 151.3333333 153 167.9 251.6 104,033.00 5.30 88253 3490.05

1 Jun-04 153.2666667 153.67 205.8666667 252.8 73,914.00 6.15 71997 3405.93

2 Sep-04 150.9333333 144 201.6333333 252.2 20,226.00 7.21 81373 4107.35

3 Dec-04 148.9 137.51 203.6333333 252.2 50,872.00 7.21 89994 4090.46

4 Mar-05 158.1 151.17 216.8333333 254.8 119,940.00 6.88 105157 4273.13

1 Jun-05 163.8333333 155.4 229.9666667 259.1333333 91,735.00 7.21 74947 3961.45

2 Sep-05 162.8666667 157.78 190.2666667 267.8 63,508.00 7.31 93883 4395.08

3 Dec-05 165.2 161.31 177 261.8 105,989.00 7.39 97953 4185.21

4 Mar-06 174.7 176.66 171.4333333 264.7666667 200,249.00 8.28 124859 4602.48

1 Jun-06 192.7666667 199.56 205.9 266.3 58,060.00 7.64 109589 4390.2

2 Sep-06 194.7 199.23 216 270.0666667 154,822.00 7.95 123165 4202.28

3 Dec-06 198.0666667 199.97 215.6 277.1666667 70,960.00 7.41 133967 4469.46

4 Mar-07 203.2 205.46 221.3 273.3666667 283,542.00 7.92 154439 5609.58

1 Jun-07 212.2666667 213.79 234.5 272.6 89,554.00 7.92 112951 4745.3

2 Sep-07 216.8333333 216.69 229.1 272.7 197,021.00 7.64 127130 4785.9

3 Dec-07 219.7666667 221.8 230.8 272.7 119,300.00 7.92 142289 4973.92

4 Mar-08 221 221.88 247.6333333 274.1 303,928.00 8.72 166806 5736.69

1 Jun-08 221.8333333 224.49 292.2666667 276.4666667 84,387.00 6 123241 6087.23

2 Sep-08 223.5333333 223.8 295.4333333 276.5 176,249.00 6.29 126348 6725.89

3 Dec-08 224.3 222.54 280.6333333 276.5 162,910.00 7.12 75391 4750.61

4 Mar-09 223.4666667 220 240.2333333 274.0666667 333,751.00 7.59 102597 6209.12

1 Jun-09 228.6333333 228.66 228.0666667 269.2 172,702.00 7.86 103844 5554.02

2 Sep-09 229.3 232.21 230.3333333 277.6666667 159,091.00 7.52 134569 5629.85

3 Dec-09 221.5666667 229.97 241.6333333 281.9 132,685.00 7.46 145297 6307.48

4 Mar-10 213.9333333 232.09 249.1 281.9 351,070.00 7.83 193088 7225.47

1 Jun-10 223.8 232.91 296.7333333 293.5 106,297.00 7.58 164066 6471.27

2 Sep-10 208 218.92 290.7 299.3 186,330.00 7.9 180919 7038.13

APPENDIX – II ACF VARIABLES=TS

/NOLOG

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes

Output Created 30-Nov-2010 12:48:48

Comments

Input Data D:\IIM Data Recovery\MBA

Related\BusF\group_project_TATAST

EELSALES.sav

Active Dataset DataSet0

Filter <none>

Weight <none>

Split File <none>

N of Rows in Working Data

File

42

Date YEAR, not periodic, QUARTER, period

4

Missing Value Handling Definition of Missing User-defined missing values are

treated as missing.

Cases Used For a given time series variable, cases

with missing values are not used in the

analysis. Also, cases with negative or

zero values are not used, if the log

transform is requested.

Syntax ACF VARIABLES=TS

/NOLOG

/MXAUTO 16

/SERROR=IND

/PACF.

Resources Processor Time 00 00:00:02.059

Elapsed Time 00 00:00:02.207

Use From First observation

To Last observation

Time Series Settings (TSET) Amount of Output PRINT = DEFAULT

Saving New Variables NEWVAR = CURRENT

Maximum Number of Lags in

Autocorrelation or Partial

Autocorrelation Plots

MXAUTO = 16

Maximum Number of Lags

Per Cross-Correlation Plots

MXCROSS = 7

Maximum Number of New

Variables Generated Per

Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000

Treatment of User-Missing

Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95

Tolerance for Entering

Variables in Regression

Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001

Method of Calculating Std.

Errors for Autocorrelations

ACFSE = IND

Length of Seasonal Period PERIOD = 4

Variable Whose Values

Label Observations in Plots

Unspecified

Equations Include CONSTANT

[DataSet0] D:\IIM Data Recovery\MBA Related\BusF\group_project_TATASTEELSALES.sav

Model Description

Model Name MOD_1

Series Name 1 TS

Transformation None

Non-Seasonal Differencing 0

Seasonal Differencing 0

Length of Seasonal Period 4

Maximum Number of Lags 16

Process Assumed for Calculating the

Standard Errors of the Autocorrelations

Independence(white noise)

Display and Plot All lags

Applying the model specifications from MOD_1

a. Not applicable for calculating the standard errors of the partial

autocorrelations.

Case Processing Summary

TS

Series Length 42

Number of Missing Values User-Missing 0

System-Missing 0

Number of Valid Values 42

Number of Computable First Lags 41

TS

Autocorrelations

Series:TS

Lag Autocorrelation Std. Errora

Box-Ljung Statistic

Value df Sig.b

1 .864 .149 33.648 1 .000

2 .811 .147 64.019 2 .000

3 .718 .145 88.430 3 .000

4 .681 .143 110.952 4 .000

5 .607 .141 129.360 5 .000

6 .584 .140 146.854 6 .000

7 .477 .138 158.860 7 .000

8 .465 .136 170.611 8 .000

9 .355 .134 177.659 9 .000

10 .281 .132 182.215 10 .000

11 .202 .130 184.649 11 .000

12 .177 .127 186.586 12 .000

13 .102 .125 187.246 13 .000

14 .069 .123 187.558 14 .000

15 -.014 .121 187.572 15 .000

16 -.042 .119 187.696 16 .000

a. The underlying process assumed is independence (white noise).

b. Based on the asymptotic chi-square approximation.

Partial Autocorrelations

Series:TS

Lag

Partial

Autocorrelation Std. Error

1 .864 .154

2 .254 .154

3 -.102 .154

4 .120 .154

5 -.066 .154

6 .096 .154

7 -.257 .154

8 .185 .154

9 -.267 .154

10 -.141 .154

11 .074 .154

12 .053 .154

13 -.078 .154

14 -.086 .154

15 .013 .154

16 -.017 .154

ACF VARIABLES=TS

/NOLOG

/DIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/DIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.936


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_2

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0


Number of Values Lost Due to Differencing 1

Number of Computable First Lags After Differencing 40

TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.539 .151 12.787 1 .000

2 .144 .149 13.722 2 .001

3 -.205 .147 15.681 3 .001

4 .247 .145 18.588 4 .001

5 -.364 .143 25.087 5 .000

6 .474 .141 36.424 6 .000

7 -.442 .139 46.556 7 .000

8 .287 .137 50.956 8 .000

9 -.140 .135 52.040 9 .000

10 .096 .133 52.569 10 .000

11 -.214 .130 55.271 11 .000

12 .321 .128 61.516 12 .000

13 -.288 .126 66.721 13 .000

14 .181 .124 68.855 14 .000

15 -.139 .121 70.159 15 .000

16 .207 .119 73.175 16 .000




Series:TS

Lag

Partial


1 -.539 .156

2 -.206 .156

3 -.328 .156

4 -.028 .156

5 -.393 .156

6 .143 .156

7 -.258 .156

8 -.071 .156

9 .013 .156

10 -.173 .156

11 -.105 .156

12 -.083 .156

13 -.064 .156

14 -.129 .156

15 -.170 .156

16 .079 .156

ACF VARIABLES=TS

/NOLOG

/SDIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/SDIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.811


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_3

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0




TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 .212 .156 1.852 1 .174

2 -.057 .154 1.987 2 .370

3 .020 .152 2.004 3 .572

4 -.517 .150 13.941 4 .007

5 -.094 .147 14.347 5 .014

6 .182 .145 15.918 6 .014

7 -.148 .143 16.998 7 .017

8 .005 .140 17.000 8 .030

9 .017 .138 17.015 9 .048

10 -.171 .136 18.594 10 .046

11 .000 .133 18.594 11 .069

12 .019 .131 18.616 12 .098

13 -.059 .128 18.828 13 .129

14 .083 .126 19.263 14 .155

15 .118 .123 20.182 15 .165

16 .042 .120 20.301 16 .207




Series:TS

Lag

Partial


1 .212 .162

2 -.106 .162

3 .059 .162

4 -.575 .162

5 .294 .162

6 -.016 .162

7 -.152 .162

8 -.295 .162

9 .173 .162

10 -.056 .162

11 -.195 .162

12 -.175 .162

13 .152 .162

14 .014 .162

15 -.053 .162

16 -.081 .162

ACF VARIABLES=TS

/NOLOG

/SDIFF=4

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/SDIFF=4

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.837


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_5

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0




TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 .250 .185 1.821 1 .177

2 -.032 .182 1.851 2 .396

3 .080 .178 2.056 3 .561

4 -.471 .174 9.402 4 .052

5 -.174 .170 10.447 5 .064

6 .154 .166 11.311 6 .079

7 -.098 .162 11.678 7 .112

8 .023 .157 11.699 8 .165

9 .009 .153 11.702 9 .231

10 -.205 .148 13.622 10 .191

11 -.085 .144 13.972 11 .235

12 -.035 .139 14.034 12 .299

13 .018 .134 14.052 13 .370

14 .192 .128 16.282 14 .296

15 .190 .123 18.671 15 .229

16 .124 .117 19.799 16 .229




Series:TS

Lag

Partial


1 .250 .196

2 -.100 .196

3 .123 .196

4 -.579 .196

5 .274 .196

6 -.020 .196

7 .008 .196

8 -.294 .196

9 .032 .196

10 -.077 .196

11 -.058 .196

12 -.163 .196

13 .146 .196

14 .069 .196

15 .112 .196

16 -.068 .196

ACF VARIABLES=TS

/NOLOG

/DIFF=1

/SDIFF=2

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/DIFF=1

/SDIFF=2

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.732


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_7

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0




TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.337 .166 4.098 1 .043

2 -.186 .164 5.380 2 .068

3 .417 .161 12.074 3 .007

4 -.471 .158 20.894 4 .000

5 .012 .156 20.899 5 .001

6 .310 .153 25.004 6 .000

7 -.264 .150 28.112 7 .000

8 .014 .147 28.121 8 .000

9 .166 .144 29.450 9 .001

10 -.180 .141 31.070 10 .001

11 .037 .138 31.142 11 .001

12 .034 .135 31.204 12 .002

13 -.072 .132 31.502 13 .003

14 .044 .128 31.621 14 .005

15 .070 .125 31.932 15 .007

16 .057 .121 32.156 16 .010




Series:TS

Lag

Partial


1 -.337 .174

2 -.337 .174

3 .280 .174

4 -.369 .174

5 -.134 .174

6 .034 .174

7 .054 .174

8 -.170 .174

9 -.039 .174

10 .018 .174

11 -.001 .174

12 -.185 .174

13 .001 .174

14 .009 .174

15 .080 .174

16 .108 .174

ACF VARIABLES=TS

/NOLOG

/DIFF=1

/SDIFF=3

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/DIFF=1

/SDIFF=3

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.770


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_9

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0




TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.321 .176 3.318 1 .069

2 -.134 .173 3.918 2 .141

3 .441 .170 10.630 3 .014

4 -.451 .167 17.929 4 .001

5 -.049 .163 18.018 5 .003

6 .291 .160 21.319 6 .002

7 -.233 .156 23.546 7 .001

8 .050 .153 23.655 8 .003

9 .137 .149 24.494 9 .004

10 -.180 .145 26.021 10 .004

11 .007 .141 26.024 11 .006

12 -.021 .138 26.047 12 .011

13 -.054 .133 26.210 13 .016

14 .058 .129 26.410 14 .023

15 .042 .125 26.524 15 .033

16 .090 .120 27.081 16 .041

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.321 .176 3.318 1 .069

2 -.134 .173 3.918 2 .141

3 .441 .170 10.630 3 .014

4 -.451 .167 17.929 4 .001

5 -.049 .163 18.018 5 .003

6 .291 .160 21.319 6 .002

7 -.233 .156 23.546 7 .001

8 .050 .153 23.655 8 .003

9 .137 .149 24.494 9 .004

10 -.180 .145 26.021 10 .004

11 .007 .141 26.024 11 .006

12 -.021 .138 26.047 12 .011

13 -.054 .133 26.210 13 .016

14 .058 .129 26.410 14 .023

15 .042 .125 26.524 15 .033

16 .090 .120 27.081 16 .041




Series:TS

Lag

Partial


1 -.321 .186

2 -.265 .186

3 .361 .186

4 -.294 .186

5 -.199 .186

6 .029 .186

7 .113 .186

8 -.024 .186

9 -.093 .186

10 -.033 .186

11 -.035 .186

12 -.162 .186

13 -.039 .186

14 .030 .186

15 .077 .186

16 .109 .186

ACF VARIABLES=TS

/NOLOG

/DIFF=1

/SDIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.

ACF

Notes


Comments



EELSALES.sav


Filter <none>

Weight <none>

Split File <none>


File

42


4


treated as missing.







/NOLOG

/DIFF=1

/SDIFF=1

/MXAUTO 16

/SERROR=IND

/PACF.


Elapsed Time 00 00:00:00.909


To Last observation






MXAUTO = 16



MXCROSS = 7



Procedure

MXNEWVAR = 60


Cases Per Procedure

MXPREDICT = 1000


Values

MISSING = EXCLUDE

Confidence Interval

Percentage Value

CIN = 95



Equations

TOLER = .0001

Maximum Iterative

Parameter Change

CNVERGE = .001



ACFSE = IND




Unspecified



Model Description

Model Name MOD_16

Series Name 1 TS

Transformation None











autocorrelations.


TS

Series Length 42


System-Missing 0




TS

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.323 .158 4.172 1 .041

2 -.240 .156 6.551 2 .038

3 .376 .153 12.546 3 .006

4 -.502 .151 23.569 4 .000

5 .073 .149 23.810 5 .000

6 .359 .147 29.813 6 .000

7 -.284 .144 33.692 7 .000

8 -.015 .142 33.704 8 .000

9 .160 .139 35.030 9 .000

10 -.183 .137 36.828 10 .000

11 .083 .134 37.211 11 .000

12 .067 .132 37.472 12 .000

13 -.131 .129 38.498 13 .000

14 .039 .126 38.594 14 .000

15 .103 .123 39.285 15 .001

16 .021 .121 39.317 16 .001

Autocorrelations

Series:TS


Box-Ljung Statistic

Value df Sig.b

1 -.323 .158 4.172 1 .041

2 -.240 .156 6.551 2 .038

3 .376 .153 12.546 3 .006

4 -.502 .151 23.569 4 .000

5 .073 .149 23.810 5 .000

6 .359 .147 29.813 6 .000

7 -.284 .144 33.692 7 .000

8 -.015 .142 33.704 8 .000

9 .160 .139 35.030 9 .000

10 -.183 .137 36.828 10 .000

11 .083 .134 37.211 11 .000

12 .067 .132 37.472 12 .000

13 -.131 .129 38.498 13 .000

14 .039 .126 38.594 14 .000

15 .103 .123 39.285 15 .001

16 .021 .121 39.317 16 .001




Series:TS

Lag

Partial


1 -.323 .164

2 -.384 .164

3 .189 .164

4 -.506 .164

5 -.110 .164

6 .021 .164

7 .043 .164

8 -.299 .164

9 -.035 .164

10 -.012 .164

11 .030 .164

12 -.240 .164

13 -.008 .164

14 -.069 .164

15 .131 .164

16 .062 .164

APPENDIX – III

ARIMA(2,0,8)(0,0,0)

Model Description

Model Type

Model ID TS Model_1 ARIMA(2,0,8)(0,0,0)

Model Summary

Fit Statistic Mean SE Minimum Maximum

Stationary R-squared .851 . .851 .851

R-squared .851 . .851 .851

RMSE 665.949 . 665.949 665.949

MAPE 12.402 . 12.402 12.402

MaxAPE 174.071 . 174.071 174.071

MAE 329.235 . 329.235 329.235

MaxAE 2439.123 . 2439.123 2439.123

Normalized BIC 14.097 . 14.097 14.097

Model Statistics

Model

Number of

Predictors

Model Fit statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-

squared Statistics DF Sig.

TS-Model_1 0 .851 5.842 8 .665 0

ERROR DIAGNOSTIC

Noise residual from TS-Model_1

Autocorrelations

Series:Noise residual from TS-Model_1


Box-Ljung Statistic

Value df Sig.b

1 -.048 .160 .089 1 .766

2 -.087 .158 .390 2 .823

3 -.127 .155 1.062 3 .786

4 .140 .153 1.895 4 .755

5 -.064 .151 2.076 5 .838

6 .040 .148 2.150 6 .905

7 -.041 .146 2.231 7 .946

8 .094 .143 2.663 8 .954

9 -.010 .140 2.668 9 .976

10 -.054 .138 2.822 10 .985

11 -.113 .135 3.523 11 .982

12 .046 .132 3.643 12 .989

13 -.089 .130 4.118 13 .990

14 .087 .127 4.592 14 .991

15 .014 .124 4.604 15 .995

16 .066 .121 4.905 16 .996

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.048 .160 .089 1 .766

2 -.087 .158 .390 2 .823

3 -.127 .155 1.062 3 .786

4 .140 .153 1.895 4 .755

5 -.064 .151 2.076 5 .838

6 .040 .148 2.150 6 .905

7 -.041 .146 2.231 7 .946

8 .094 .143 2.663 8 .954

9 -.010 .140 2.668 9 .976

10 -.054 .138 2.822 10 .985

11 -.113 .135 3.523 11 .982

12 .046 .132 3.643 12 .989

13 -.089 .130 4.118 13 .990

14 .087 .127 4.592 14 .991

15 .014 .124 4.604 15 .995

16 .066 .121 4.905 16 .996





Lag

Partial


1 -.048 .167

2 -.089 .167

3 -.137 .167

4 .120 .167

5 -.077 .167

6 .042 .167

7 -.018 .167

8 .068 .167

9 .020 .167

10 -.064 .167

11 -.089 .167

12 .003 .167

13 -.117 .167

14 .073 .167

15 .027 .167

16 .046 .167

ARIMA(5,1,13)(0,0,0)

Model Description

Model Type


Model Summary

Model Fit



R-squared .956 . .956 .956

RMSE 462.990 . 462.990 462.990

MAPE 7.556 . 7.556 7.556

MaxAPE 36.948 . 36.948 36.948

MAE 266.871 . 266.871 266.871

MaxAE 888.959 . 888.959 888.959

Normalized BIC 13.996 . 13.996 13.996

ERROR DIAGNOSTIC Noise residual from TS-Model_1

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.067 .151 .200 1 .654

2 -.034 .149 .251 2 .882

3 -.048 .147 .357 3 .949

4 .004 .145 .358 4 .986

5 -.014 .143 .367 5 .996

6 .041 .141 .451 6 .998

7 -.159 .139 1.763 7 .972

8 .051 .137 1.900 8 .984

9 -.045 .135 2.011 9 .991

10 -.080 .133 2.375 10 .993

11 -.100 .130 2.969 11 .991

12 .030 .128 3.024 12 .995

13 -.084 .126 3.464 13 .996

14 .026 .124 3.509 14 .998

15 -.025 .121 3.550 15 .999

16 .066 .119 3.860 16 .999

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.067 .151 .200 1 .654

2 -.034 .149 .251 2 .882

3 -.048 .147 .357 3 .949

4 .004 .145 .358 4 .986

5 -.014 .143 .367 5 .996

6 .041 .141 .451 6 .998

7 -.159 .139 1.763 7 .972

8 .051 .137 1.900 8 .984

9 -.045 .135 2.011 9 .991

10 -.080 .133 2.375 10 .993

11 -.100 .130 2.969 11 .991

12 .030 .128 3.024 12 .995

13 -.084 .126 3.464 13 .996

14 .026 .124 3.509 14 .998

15 -.025 .121 3.550 15 .999

16 .066 .119 3.860 16 .999





Lag

Partial


1 -.067 .156

2 -.038 .156

3 -.053 .156

4 -.004 .156

5 -.018 .156

6 .036 .156

7 -.156 .156

8 .032 .156

9 -.051 .156

ARIMA(4,0,4)(0,1,0)

Model Description

Model Type


Model Summary

Model Fit



R-squared .946 . .946 .946

RMSE 411.566 . 411.566 411.566

MAPE 7.772 . 7.772 7.772

MaxAPE 29.703 . 29.703 29.703

MAE 286.839 . 286.839 286.839

MaxAE 897.260 . 897.260 897.260

Normalized BIC 12.901 . 12.901 12.901

Model

Number of

Predictors

Model Fit

statistics Ljung-Box Q(18)

Number of

Outliers

Stationary R-


TS-Model_1 0 .609 7.161 10 .710 0


Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 .107 .156 .473 1 .492

2 .077 .154 .722 2 .697

3 .053 .152 .845 3 .839

4 -.050 .150 .956 4 .916

5 .058 .147 1.112 5 .953

6 .139 .145 2.032 6 .917

7 .028 .143 2.070 7 .956

8 -.120 .140 2.795 8 .947

9 -.119 .138 3.541 9 .939

10 -.147 .136 4.709 10 .910

11 -.003 .133 4.709 11 .944

12 -.105 .131 5.352 12 .945

13 -.156 .128 6.832 13 .911

14 -.042 .126 6.945 14 .937

15 .007 .123 6.948 15 .959

16 -.010 .120 6.955 16 .974

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 .107 .156 .473 1 .492

2 .077 .154 .722 2 .697

3 .053 .152 .845 3 .839

4 -.050 .150 .956 4 .916

5 .058 .147 1.112 5 .953

6 .139 .145 2.032 6 .917

7 .028 .143 2.070 7 .956

8 -.120 .140 2.795 8 .947

9 -.119 .138 3.541 9 .939

10 -.147 .136 4.709 10 .910

11 -.003 .133 4.709 11 .944

12 -.105 .131 5.352 12 .945

13 -.156 .128 6.832 13 .911

14 -.042 .126 6.945 14 .937

15 .007 .123 6.948 15 .959

16 -.010 .120 6.955 16 .974





Lag

Partial


1 .107 .162

2 .066 .162

3 .039 .162

4 -.065 .162

5 .065 .162

6 .136 .162

7 -.002 .162

8 -.158 .162

9 -.107 .162

10 -.096 .162

11 .041 .162

ARIMA(0,1,4)(0,4,0)

Model Description

Model Type


Model Summary

Model Fit



R-squared -3.610 . -3.610 -3.610

RMSE 2394.788 . 2394.788 2394.788

MAPE 30.224 . 30.224 30.224

MaxAPE 98.440 . 98.440 98.440

MAE 1605.532 . 1605.532 1605.532

MaxAE 6209.095 . 6209.095 6209.095

Normalized BIC 16.206 . 16.206 16.206

Model Statistics

Model

Number of

Predictors

Model Fit


Number of

Outliers

Stationary R-


TS-Model_1 0 .562 19.103 14 .161 0


Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.122 .189 .421 1 .517

2 -.131 .185 .927 2 .629

3 .160 .181 1.711 3 .634

4 -.403 .176 6.922 4 .140

5 -.008 .172 6.924 5 .226

6 .227 .168 8.757 6 .188

7 -.176 .163 9.914 7 .193

8 .035 .159 9.964 8 .268

9 .081 .154 10.239 9 .332

10 -.123 .149 10.918 10 .364

11 -.003 .144 10.918 11 .450

12 -.119 .139 11.655 12 .474

13 -.086 .133 12.068 13 .522

14 .109 .128 12.791 14 .543

15 .121 .122 13.778 15 .542

16 .136 .115 15.175 16 .512

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.122 .189 .421 1 .517

2 -.131 .185 .927 2 .629

3 .160 .181 1.711 3 .634

4 -.403 .176 6.922 4 .140

5 -.008 .172 6.924 5 .226

6 .227 .168 8.757 6 .188

7 -.176 .163 9.914 7 .193

8 .035 .159 9.964 8 .268

9 .081 .154 10.239 9 .332

10 -.123 .149 10.918 10 .364

11 -.003 .144 10.918 11 .450

12 -.119 .139 11.655 12 .474

13 -.086 .133 12.068 13 .522

14 .109 .128 12.791 14 .543

15 .121 .122 13.778 15 .542

16 .136 .115 15.175 16 .512





Lag

Partial


1 -.122 .200

2 -.148 .200

3 .128 .200

4 -.406 .200

5 -.058 .200

6 .105 .200

7 -.081 .200

8 -.116 .200

9 -.012 .200

10 .028 .200

ARIMA(4,1,6)(0,1,0)

Model Description

Model Type


Model Summary

Model Fit



R-squared .932 . .932 .932

RMSE 471.268 . 471.268 471.268

MAPE 7.149 . 7.149 7.149

MaxAPE 22.242 . 22.242 22.242

MAE 295.605 . 295.605 295.605

MaxAE 1056.621 . 1056.621 1056.621

Normalized BIC 13.384 . 13.384 13.384

Model Statistics

Model

Number of

Predictors

Model Fit


Number of

Outliers

Stationary R-


TS-Model_1 0 .694 6.913 8 .546 0


Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.042 .158 .071 1 .790

2 -.091 .156 .411 2 .814

3 -.122 .153 1.039 3 .792

4 -.195 .151 2.709 4 .608

5 -.028 .149 2.743 5 .739

6 .138 .147 3.628 6 .727

7 .074 .144 3.888 7 .793

8 -.072 .142 4.148 8 .844

9 -.062 .139 4.346 9 .887

10 -.102 .137 4.903 10 .898

11 .077 .134 5.231 11 .919

12 .001 .132 5.231 12 .950

13 -.058 .129 5.432 13 .964

14 .027 .126 5.479 14 .978

15 .089 .123 5.993 15 .980

16 .057 .121 6.217 16 .986

Autocorrelations



Box-Ljung Statistic

Value df Sig.b

1 -.042 .158 .071 1 .790

2 -.091 .156 .411 2 .814

3 -.122 .153 1.039 3 .792

4 -.195 .151 2.709 4 .608

5 -.028 .149 2.743 5 .739

6 .138 .147 3.628 6 .727

7 .074 .144 3.888 7 .793

8 -.072 .142 4.148 8 .844

9 -.062 .139 4.346 9 .887

10 -.102 .137 4.903 10 .898

11 .077 .134 5.231 11 .919

12 .001 .132 5.231 12 .950

13 -.058 .129 5.432 13 .964

14 .027 .126 5.479 14 .978

15 .089 .123 5.993 15 .980

16 .057 .121 6.217 16 .986





Lag

Partial


1 -.042 .164

2 -.093 .164

3 -.131 .164

4 -.223 .164

5 -.088 .164

6 .071 .164

7 .027 .164

8 -.106 .164

9 -.068 .164

10 -.086 .164

APPENDIX – IV

Variables Entered/Removedb

Model Variables Entered

Variables

Removed Method

1 CI, Y, M3, EL, ST,

CS

. Enter

Model Summaryb

Model R R Square

Adjusted R

Square

Std. Error of the

Estimate Durbin-Watson

1 .974a .949 .938 362.71046 1.970

a. Predictors: (Constant), CI, Y, M3, EL, ST, CS

b. Dependent Variable: TS

ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 70789330.809 6 11798221.801 89.680 .000a

Residual 3815207.373 29 131558.875

Total 74604538.181 35

a. Predictors: (Constant), CI, Y, M3, EL, ST, CS

b. Dependent Variable: TS

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) -1936.427 1322.093 -1.465 .154

ST -11.436 2.438 -.465 4.690 .000

M3 .002 .001 .134 2.146 .040

CS .010 .004 .263 2.646 .013

EL 9.995 5.833 .169 1.714 .097

Y -62.820 89.928 -.037 -.699 .490

CI 2.450 4.691 .054 .522 .605

ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 70789330.809 6 11798221.801 89.680 .000a

Residual 3815207.373 29 131558.875

Total 74604538.181 35

a. Dependent Variable: TS

Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N

Predicted Value 1638.5338 6049.4902 3675.2163 1422.16466 36

Residual -614.99127 743.60608 .00000 330.16045 36

Std. Predicted Value -1.432 1.669 .000 1.000 36

Std. Residual -1.696 2.050 .000 .910 36

a. Dependent Variable: TS

The views expressed above are the views of the author and do not necessarily represent the

views of any organisation.

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Data & Analytics

Forecasting model primer_v1