Measuring the Synchronization of Bull and Bear

Markets in Canadian Housing Prices

(Preliminary version)

Christos Ntantamis ∗

Dalhousie University

October 27, 2016

Abstract

This paper investigates the level of synchronization of the housing markets of Cana-

dian metropolitan areas. By utilizing the House Price Index developed by Teranet in

alliance with National Bank, which is available for 11 major Canadian cities, two dif-

ferent market regimes are identified. A bull market regime (a longer period of rise in

prices), and a bear market regime (a longer period of decline in prices) are obtained

by employing the Lunde and Timmermann (2004) data-based algorithm. The degree

of synchronization is estimated using the Candelon et al. (2009) methodology; their

approach allows for an imperfect degree of multivariate synchronization between mar-

ket cycles. Besides investigating the synchronization among housing market cycles of

Canadian cities, I also explore their degree of synchronization with macroeconomic and

financial variables, such as interest rates and commodity prices. The findings point to

low degrees of synchronization, especially among the group of the larger metropolitan

areas.

Keywords: House Price Index; Bull and Bear Markets; Degree of Synchronization

JEL Classification Numbers: C22, E32, R30

∗Address: Department of Economics, Dalhousie University, 6214 University Ave, Halifax, NS, B3H4R2,Canada, telephone: +1-902-4948945, email: christos.ntantamis@dal.com.

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1 Introduction

House prices have risen markedly in Canada during the recent years, and concerns has been

raised in the public media of whether the market experiences a bubble, similar to the one

that United States were experiencing prior to 2007. If this is the case, policy changes are

required to reduce the possibility of it bursting. However, even though such policies are

anticipated to have any effect on house prices, we cannot be certain of whether this effect

will be uniform across all metropolitan areas. To answer this question, it is important to

have a measure of the degree that housing markets across Canada are synchronized, i.e.,

they exhibit similar behaviour over time.

In this paper, the approach first proposed by Harding and Pagan (2006), and extended by

Candelon et. al. (2009) is followed in defining and estimating synchronization across markets.

This approach measures the amount of bivariate bull and bear market cycles synchronization

by Pearson-type correlations on the binary variables that represent the different market

phases. Using a GMM-based multivariate procedure, Candelon et al (2009) consider the

null hypothesis to be that of strong (but imperfect) multivariate synchronization with all

bivariate correlations to be equal.

Many empirical studies have demonstrated that house prices are subject to quite frequent

boom-and-bust cycles (e.g., Bordo and Jeanne, 2002). The empirical literature on housing

markets recognizes the importance of swings in housing prices and their relationship to

changes in the liquidity of the market; Muellbauer and Murphy (1997) and Herring and

Wachter (1999) explicitly refer to booms and busts in housing prices and admit the non-

linearities that they imply. The studies by Englund and Ioannides (1997), Capozza et al.

(2002), Tsatsaronis and Zhu (2003), and Borio and Mcguire (2004), among others, report

significant correlations between real housing price growth and variables such as real GDP,

and interest rates.

This paper employs the Teranet - National Bank House Price Index as a proxy for Hous-

ing Price Index, which is based on the rate of change of Canadian housing prices. The data

set includes monthly indices for eleven Canadian metropolitan areas: Victoria, Vancouver,

Calgary, Edmonton, Winnipeg, Hamilton, Toronto, Ottawa, Montreal, Quebec and Halifax.

Additionally, the Bank of Canada Commodity Index, the oil price (Western Texas Interme-

diate), and the 5-year Benchmark bond yield are also included to examine synchronization

with commodity markets and interest rates.

The first step of the analysis is to identify the bull and bear markets for each each series.

To that end, I employ the Lunde and Timmermann (2004) algorithm. A key advantage of

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this data-based identification algorithm is that it does not impose any model structure on

the data. It defines bull/bear markets as periods where prices do not deviate much from the

local peak/trough of the current market. Our analysis is conducted in two steps. The first

step is to identify and examine the bull and bear markets for each series respectively. In par-

ticular, we examine the durations of the bull and bear market phases, and the distributional

characteristics of the series’ returns under each phase. The second step involves applying

the Candelon et al. (2009) GMM-based test to recover the degree of synchronization among

metropolitan areas and commodity prices that are of interest and make intuitive sense (e.g.

the degree of synchronization of the housing markets of Calgary and Edmonton with oil

prices).

Anticipating the results, I find little support for multivariate synchronization of housing

markets in Canada, with the exception of selected metropolitan areas that share similar

characteristics in terms of their economies. Commodity prices and interest rates also do

not exhibit large degrees of synchronization, contrary to the what is widely believed in the

popular press.

The paper is organized as follows. Section 2 discusses the methodology for the identifica-

tion of the bull/bear markets. Presentation of the data and discussion of results is provided

in Section 3, and Section 4 concludes the paper.

2 Methodology

2.1 Identifying Bull and Bear Markets

Data-based identification is mainly concerned with converting the rather abstract notion

of ”rising/declining” stock (or other asset) prices into more quantitative criteria enabling

the construction of actual identification algorithms. Some of the first of such criteria are

introduced by Fabozzi and Francis (1977). They suggest a definition of bull/bear markets

in terms of critical bounds for the stock returns. Among other things, they defined bull and

bear markets as periods during which returns are above zero and below zero respectively.

They also considered definitions where returns within plus/minus one half standard deviation

were excluded, those above this interval were labeled ”bull”, and those below were labeled

”bear”. Similarly, Kim and Zumwalt (1979) also define bull/bear markets in terms of the

returns. Bull markets are defined as periods where returns exceed either the average return,

or the risk free return, or zero, the remaining periods being identified as bear markets.

It can be noticed that both of these approaches rely on returns sharing some common

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underlying characteristics throughout the entire sample (such as common mean, common

standard deviation, or the like), and detect bull/bear markets as extremes within this set

of returns.This is also a definition of bull/bear markets when Regime Switching models are

used (Schaller and van Norden 1997), with the exception that in these models the threshold

values for the returns are endogenously estimated by the models themselves.

An alternative definition, which is less restrictive, for bull and bear markets is based on

the local traits of asset prices. Bull and bear markets are defined as periods when prices are

not too far away from the local peak/trough of the current market. Therefore, bull/bear

markets are detected relative to the characteristics of the current market and not to the

entire sample. This approach has been used by Pagan and Sossounov (2003) and Lunde

and Timmermann (2004). Pagan and Sossounov (2003) use a modification of the Bry and

Boschan (1971) algorithm, who pose constraints on the durations of market phases and of

market cycles.

2.2 The Lunde-Timmerman Algorithm

The Lunde and Timmermann (2004) data-based algorithm, henceforth LT-algorithm, is used

in this paper due to its advantages. First, compared to Pagan and Sossounov (2003) who

constrain the durations, LT-algorithm does not impose any such restrictions. Second, this

algorithm does not define bull/bear markets in terms of the returns’ characteristics unlike

Fabozzi and Francis (1977) and Kim and Zumwalt (1979), or using parametric models such

as Hamilton (1989) Markov Regime Swithcing models. Furthermore, it is already used

extensively in the finance literature (Chiang and Huang 2011; Maheu et al. 2012)

The LT-algorithm provides a rule that one can iterate in order to determine whether an

observation belongs to a bull/bear market. The algorithm can be described as follows:

Let pmin be the smallest of the prices so far observed in a current bear market and pmax

be the largest of the prices so far observed in a current bull market. Denote by λ1 and λ2

the critical percentages (filters) of the bear and bull markets respectively. For each of the

two states the preceding price can belong to, one of three things will happen:

• Bull state:

– pmax < p: The bull market continues, and p becomes the new pmax

– pmax (1− λ2) < p ≤ pmax: The bull market continues, and there is no change in

the value of pmax

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– p ≤ pmax (1− λ2): The bull market terminates and is replaced by a bear market

with p as its first observation. Furthermore, p is the pmin of this bear market.

• Bear state:

– p < pmin: The bear market continues, and p is the new pmin

– pmin ≤ p < pmin (1 + λ1): The bear market continues, and there is no change in

the value of pmin

– pmin (1 + λ1) ≤ p: The bear market terminates and is replaced by a bull market

with p as its first observation. Furthermore, p is the pmax of this bull market.

Putting it in words, the algorithm considers a change from a bull (bear) to a bear (bull)

market if the price drops (increases) by more than a pre-specified percentage. As a result of

this definition, we may observe price declines (increases) during a bull (bear) market.

Figure 1: Mechanics of the Lunde and Timmermann (2004) Algorithm

There are two main implementation issues for the LT-algorithm: i) the choice of filters,

and ii) short-term fluctuations and filtering. If there is a drift in the stock price series from

which one derives the bull/bear markets, one has to adjust the filter (λ1, λ2) so as to account

for this (Lunde and Timmermann, 2004). In particular, if the series exhibits an upward

trend, an asymmetric filter with λ1 > λ2 is required so that in order to move from a bear

market to a bull market, the stock price would have to increase more than it would have to

decrease to go the other way.

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Given the sensitivity of the method to the choice of filters, it has been argued that

choosing a variant of the Bry and Boschan (1971) algorithm, which is used more frequently in

the economics literature ( e.g. stock market prices: Pagan and Sossounov 2003, Harding and

Pagan 2006, Candelon et al. 2008, 2009, and commodity prices: Cashin et al. 2002, Roberts

2009), may be prefereable. Regardless, the Bry-Boschan algorithm still requires making a

number of assumptions such as the minimum durations and the smoothness parameters.By

using the LT-algorithm in this paper we do not restrict minimum duration values of bull and

bear markets, and hence gain more flexibility.

2.3 Measuring the synchronization of Bull and Bear Markets

Different approaches to measuring the synchronization of market have been put forward

in the literature. In this paper, we follow the approach first proposed by Harding and

Pagan (2006), and extended by Candelon et. al. (2009). This approach measures the

amount of bivariate market cycles synchronization by Pearson-type correlations on binary

variables representing different market phases. Whereas Harding and Pagan (2006) GMM-

based multivariate procedure examines the null hypothesis that business cycles are either

perfectly synchronized (all bivariate correlations equal to 1) or not synchronized at all (all

bivariate correlations equal to 0), Candelon et al (2009) consider the null hypothesis to be

that of strong (but imperfect) multivariate synchronization with all bivariate correlations to

be equal but within the (−1, 1) range.

2.3.1 Candelon et al. 2006 Methodology

Assume that after applying a bull and bear market identification algorithm, like the L-

T algorithm used in this paper, we have obtained the indicator variables Sit such that

Sit = 1 when the ith series is in a bull market and Sit = 0 when the ith series is in a bear

market, for each of the n markets we are interested in. Candelon et al. (2009) proposed

a general framework to test for the existence of multivariate synchronization of degree ρ0

(−1 < ρ0 < 1).

The procedure starts with the following moment conditions:

E [ht (θ0, St)] = 0 (1)

where

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ht (θ, St) =

S1t − µ1

...

Snt − µn(S1t−µ1)(S2t−µ2)√µ1(1−µ1)µ2(1−µ2)

− ρ12...

(Sn−1t−µn−1)(Snt−µn)√µn−1(1−µn−1)µn(1−µn)

− ρ(n−1)n

(2)

and with θ′

=[µ1, . . . , µn, ρ12, . . . , ρ(n−1)n

]is the vector of unrestricted parameters. The

first subset of n moments defines the population means of the market indicator variables.

As such, they correspond to the unconditional likelihood of the series being in a bull market.

The second subset of n(n − 1)/2 moments corresponds to all bivariate correlations. Under

the null hypothesis of strong multivariate synchronization of degree ρ0 (SMS(ρ0)), i.e., all

bivariate correlations are equal to ρ0, the restricted parameter vector can now be written as:

θ′0 =

[µ1, . . . , µn, ρ0, . . . , ρ(0

]. That is, all markets exhibit a common synchronization.

In order to test for SMS(ρ0), the following Wald test statistic is used:

W (ρ0) = Tg(θ0, [S]Tt=1

)′V̂ −1g

(θ0, [S]Tt=1

)(3)

which converges to an asymptotic χ2n(n−1)/2 distribution under the null hypothesis (θ =

θ0). The covariance matrix V̂ is a heteroskedasticity and autocorrelation consistent estimator

(HAC) of the variance-covariance matrix of√Tg(θ0, [S]Tt=1

). The statistic is defined as a

quadratic form in the penalty vector g(θ0, [S]Tt=1

)= 1

T

∑Tt=1 ht (θ0, St), which reflects the

average deviation from the moment conditions.

There are two issues. The first one is that the implementation of the Wald test depends

upon a value for the (unknown) parameter ρ0. This addressed by considering a two-step

procedure. First, determine a closed interval [ρ−, ρ+] for which SMS(ρ0) cannot be rejected

at a prespecified nominal size. Second, a natural estimator for ρ0 follows by minimizing the

test statistic over the obtained range:

ρ̂0 = argminρ∈[ρ−,ρ+]W (ρ) (4)

The second issue is related to the small size properties of the SMS(ρ0) test. Candelon et

al. (2009) identified via a simulation exercise that significant size distortions are present if

one were to use the asymptotic critical values. As a consequence, the null hypothesis would

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be rejected too often. Consequently, they propose using a bootstrap to generate the small

sample distribution of the GMM test; they consider a non-parametric block bootstrap.

The process, as adapted in this paper can be described as follows:

1. Generate a T ×n matrix of bootstrap replications SB by randomly draw b consecutive

St with replacement (b is the size of the block, and set to 24 to correspond to 2 years

of data, and of similar magnitude to the number employed in Candelon et al. 2008

and 2009).

2. Ensure that the average number of bull/bear market cycles observed for the bootstrap

samples, cynoboot, falls within the range[0.95cynodata, 1.05cynodata], where cynodata is

the number of cycles for the observed data; we discard any bootstrap sample that fails

this condition.

3. Compute the bootstrapped Wald statistic for ρ0, i.e. WB (ρ0), using SB as an input.

4. Repeat steps 1-3 above for a sufficient number of times. In this paper, we consider

the total number of bootstrap replications to be equal to 199. We can then compute

the critical value as the 5% quantile, say WBCV , from the empirical distribution of the

bootstrap test statistic.

5. The null hypothesis is rejected if W (ρ0) > WBcv .

3 Empirical Analysis

3.1 Data

This paper employs the Teranet - National Bank House Price Index as a proxy for Housing

Price Index. The index is based on the rate of change of Canadian housing prices, based

on actual sale transactions 1. The data set includes monthly indices cover for eleven Cana-

dian metropolitan areas: Victoria, Vancouver, Calgary, Edmonton, Winnipeg, Hamilton,

Toronto, Ottawa-Gatineau, Montreal, Quebec and Halifax (see Table 1 for the dates when

the indices are available). These metropolitan areas are combined to form two national com-

posite indices: one that includes 6 metros(Composite 6), which includes Vancouver, Calgary,

1The index is estimated by tracking the observed or registered home prices over time. Properties with atleast two sales are required in the calculations (repeat sales methodology).

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Toronto, Ottawa-Gatineau, Montreal, Halifax, and one that includes all metros (Composite

11)2.

The indices are not seasonally adjusted, and thus employing them in our estimation of

the bull and bear markets may produce transitions generated due to seasonal patterns (e.g.

depressed prices during the winter months). Consequently, I proceed in seasonally adjusting

them. Furthermore, since I am also interested in real housing prices, a measure for inflation

is used to adjust the nominal housing prices indices (Canadian headline Consumer Price

Index).

The commodity series used in this paper are the oil price (Western Texas Intermediate)

and the Bank of Canada Commodity Index (BCPI). The latter is a chain Fisher price index of

the spot or transaction prices in U.S. dollars of 24 commodities (energy, metals and minerals,

fisheries, agriculture, and forestry) produced in Canada and sold in world markets. Finally,

I consider the 5-year Benchmark bond yield to generate the cycles in interest rates 3.

Figures 2 and 3 depict the House Price Indices, in nominal and in real terms, for the two

composite measures (set to 100 on March 1999), whereas Figure 4 shows the nominal and

real HPI for each metropolitan areas.. The overall pattern is the same regardless of whether

the nominal or real values are examined. There are two main observations to be drawn: i)

house prices started increasing faster after 2000, and ii) there is a sharp increase taking place

in Calgary and Edmonton after 2006 and till 2008. Given that the values of the indices are

different across the areas, the actual values are not directly comparable.

To facilitate comparisons, in Figure 5 all indices were standardized to be equal to 100 in

March 1999, when data for all metropolitan areas became available. Furthermore, the areas

are separated into three graphs; Vancouver, Victoria, Calgary, Edmonton, and Winnipeg

are depicted in the “Western Canada” graph, the other metros are depicted in the “Eastern

Canada” graph, and finally the 6 metros that comprise the composite-6 index are depicted

in the third. It can be noticed that house price increases were larger, either in nominal or

real terms, in the West compared to the East. Montreal and Quebec appear to experience

larger price increases compared to the other “eastern” metropolitan areas 4. Focusing on

the composite-6 metropolitan areas, two things stand out. First, the dramatic increase and

subsequent decrease in prices for Calgary before and after the 2008 Great Recession, widely

2The data used in the paper were obtained via the HAVER database.3The most common mortgage in Canada has a fixed interest rate for a 5-year term (Crawford et al. 2013).4This is not a surprise: examining carefully the price indices for these two cities, one can observe that

a decline was experienced during the 90’s, due to the concerns for the Quebec independence referendum.Thus, the subsequent increase was more significant as it started from a lower base.

9

associated with the oil price movements. Second, the outperformance of the Vancouver

housing market relative to the other metros.

The descriptive statistics for the monthly returns, nominal and real, of all house price

indices and commodity and interest rate series are provided in Table 2. The following remarks

can be made: a) the average returns are relatively low, b) the coefficient of variations are

on average larger for real returns, c) most return series exhibit excess kurtosis, i.e. there is

higher probability for extreme values (especially true for Edmonton, Montreal and Ottawa-

Gatineau), and d) commodity prices are more volatile (using the coefficient of variations as

a measure), and especially so when considered in real terms.

3.2 Results

When the LT-algorithm was presented, a discussion was provided about the choice of the

threshold parameters (λ1, λ2). There are two major concerns: a) the magnitude of the pa-

rameters, which determines how frequently switches between markets occur, and b) whether

we should consider an asymmetric filter to account for an upward trend.

In this paper, I use the following approach to determine the magnitude of the parameters5. For each price index, I calculate the mean and the standard deviation of its positive and

its negative returns, (µ+, σ+) and (µ−, σ−) respectively. The parameters are then set as:

λ1 = µ+ + σ+

λ2 = |µ−|+ σ−

In most cases, this approach also yields asymmetric filters. The resulted parameters can

be found in Table 3.

The application of the LT-algorithm in each series generates a sequence of ones, when

the prices are identified to belong to a bull market, and zeros, when the prices are identified

to belong to a bear market6. In what follows, I briefly discuss the bull and bear market

properties in terms of their durations, and their returns’ distributional characteristics.

5Alternative approaches, including setting market duration criteria similar to Pagan and Sossounov(2003), yielded similar results.

6The L-T algorithm had to be modified in order to generate bull and bear market for the bond yield (uselevel changes instead of percentage changes ).

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3.2.1 Bull and Bear Market Properties

The distributional characteristics of the nominal (real) returns under the bull and the bear

markets are provided in Table 4 (5). The returns during the bull market phase have a

positive mean compared to a negative mean during the bear market phase: this is something

to be expected based on our definition of bull/bear markets. On the other hand, the returns’

variance provides less systematic results. A higher variance is observed under a bull market

for the metropolitan areas located in the “Western Canada” and for the Quebec, the opposite

result being true for the other areas, i.e. a higher variance under the bear regime. Regardless,

the coefficients of variation are on average larger under the bear market phase, almost double

from the ones for the bull market. Considering the distributions’ higher moments, skewness

is found to be positive for the bull market returns and negative for the bear market returns

for most series.

The average durations of the bull and bear markets are provided in Table 6. The average

duration for a bull market phase is higher compared to the average duration of a bear market

phase., with durations being overall smaller when considering the real series. Market phase

durations are relatively smaller for BCPI and WTI. Looking on the bull/bear markets for

the Benchmark 5-year bond yield, average durations are significantly smaller and opposite

to all other series higher for the case of the bear market.

Figures 6 and 7 depict bull and bear markets along with the relevant price index, in

nominal terms, for all metropolitan areas (bull market marked as the shaded area). A simple

visual inspection confirms that there are far more transitions for the commodity series and

the interest rate.

3.2.2 Synchronization Results

The parameter estimates for the population means (µi) and the bivariate correlations (ρi,j)

for the bull and bear market binary series obtained via the LT-algorithm are reported in

Tables 9 and 10. As it was discussed in the previous sections, the average durations of bull

markets are higher, thus we observe relatively high value for the population means, which is

the probability of a series being in a bull market. In general, we do not observe very large

bivariate correlations for the markets generated using either nominal or real prices. For the

“nominal” markets, and using a value of 0.375 as benchmark, the highest correlation (0.832)

is observed for the Calgary and Edmonton markets, whereas the second largest (0.639) is

observed for the Ottawa-Gatineau and Winnipeg market. Furthermore, Winnipeg displays

large correlations with Montreal and Quebec.

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Instead of checking all potential combinations of metropolitan areas, I restrict my analysis

to selected cases that are of interest and that make intuitive sense. The results that are

produced using bull and bear markets based on nominal prices are presented in Table 7. I

consider groups of 3 (Panel A), 4 (Panel B), and 5 (Panel C) series.

The five-series group includes Vancouver, Calgary, Toronto, Montreal and Halifax, i.e.,

the largest metropolitan areas representing the different parts of Canada. Examination the

synchronization of the markets for this groups provides a gauge about the degree that housing

market follow similar cycles across Canada. The outcome of the test points to a rejection of

synchronization: there is no value of ρ, for which we do not reject the null hypothesis that

all bivariate correlations are equal7.

Turning out attention to the four-series groups, we do not reject multivariate synchroniza-

tion, albeit of very small magnitude. Consider the group of Vancouver, Calgary, Montreal,

and Toronto, which are Canada’s largest metropolitan areas. The degree of synchronization

is equal to 0.19, and based on the (ρ−, ρ+) range even the case of no synchronization at all

cannot be rejected. The largest degree of synchronization, 0.37, is obtained for the Halifax,

Ottawa-Gatineau, Quebec and Winnipeg group. Given that this metropolitan areas share

similar demographic characteristics, and their economies rely on government services for the

first three, and on services in general for the Winnipeg. In fact, it is the only group for

where no synchronization is rejected outright. The degree of any impact that commodity

prices may have on housing is examined in two other groups that include BCPI and/or oil

prices. The case of the metropolitan areas located in the Prairies along with BCPI yielded

a synchronization degree of 0.09, the lowest value across all the groups I examined. Finally,

there is a small degree of synchronization of interest rates with housing markets either in

the 3 largest Canadian metros (Vancouver, Toronto, Montreal) or in the 3 Canadian metros

more heavily relying on government services (Halifax, Ottawa-Gatineau, and Quebec).

Panel A presents the degree of synchronization for groups of 3 series. Vancouver, Toronto

and Montreal display the lowest degree of synchronization (0.15), whereas Ottawa-Gatineua,

Montreal and Quebec the highest (0.33). As in the case of 4 metros, a relatively high

degree is obtained for the Halifax, Ottawa-Gatineau, and Quebec metropolitan areas group.

Interestingly enough, the degree of synchronization of bull and bear markets of oil price and

of housing prices in Calgary and Edmonton is relatively low, and equal to 0.18; we cannot

reject the hypothesis of no synchronization at all. One potential explanation for this finding

is that there is a significantly larger number of transitions between bull and bear market for

7The result remains the same if one substitutes Edmonton for Calgary.

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oil compared to the housing markets (see Figure 6(c),(d) for Calgary and Edmonton and

Figure 7(b) for oil prices. As a result, the degree of synchronization is found to be small 8.

The above discussion does not change when considering the degree of synchronization

between bull and bear market calculated using real prices (Table 8).

4 Conclusion

This paper investigates the synchronization among the housing markets of Canadian metropoli-

tan areas. In particular, using housing indices developed by Teranet in alliance with National

Bank, it uses the Lunde and Timmermann (2004) data-based algorithm to identify their bull

and bear market phases, before employing the Candelon et al. (2009) methodology to test

for their degree of synchronization. The Candelon et al (2009) approach consider the null hy-

pothesis to be that of strong (but imperfect) multivariate synchronization with all bivariate

correlations to be equal but within the (−1, 1) range.

By considering different groups of metropolitan areas, the results suggest a low level of

synchronization for most cases; the main exception is the group that includes metros that are

of very similar characteristics in terms of their economies, such as Halifax, Ottawa-Gatineau

and Quebec.When examining the case of metropolitan areas and commodity prices, I find

that there is a low degree of synchronization, and in fact, we cannot reject that there is no

synchronization at all. Finally, we find little synchronization between bull and bear phases

of housing markets and of interest rates.

The results of the paper that suggest that there is almost no synchronization point to

the important policy implication that there is no room for “one-size-fits-all” policies towards

housing markets. For example, if one is concerned about the probability that Toronto and

Vancouver experiencing a bull in their housing market, any policies to address such a concern

need not have the same implications for the other housing markets.

8The results may be different if one were to consider larger parameter thresholds for the LT algorithm foroil prices, thus generating a smaller number of market phases, which in turn would only occur when priceschange dramatically (e.g. during the 2008 crisis).

13

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Muellbauer, J., and A. Murphy, (1997). Booms and busts in the UK housing market, Eco-

nomic Journal, 107, 1701-1727.

Pagan A.R., and K.A. Sossounov, (2003). A Simple Framework for Analysing Bull and Bear

Markets, Journal of Applied Econometrics, 18, 23-46.

Roberts M.C., (2009). Duration and Characteristics of Metal Price Cycles, Resources Policy,

34, 87-102.

Schaller H., and S. van Norden, (1997). Regime Switching in Stock Market Returns, Applied

Financial Economics, 7, 177-191.

Tsatsaronis, K., and H. Zhu, (2003). What drives housing price dymanics: cross- country

evidence, BIS Quartely Review, March, 65-78.

15

A Data

A.1 Data Range

Index available from Index available fromComposite Index (6 cities) Feb-99 Hamilton (ON) Jul-98

Composite Index (11 cities) Mar-99 Toronto (ON) Jul-98Victoria (BC) Jul-90 Ottawa (Gatineau QC) Jul-98

Vancouver (BC) Jul-90 Montreal (QC) Jul-90Calgary (AB) Feb-99 Quebec (QC) Jul-90

Edmonton (AB) Mar-99 Halifax (NS) Jul-90Winnipeg (MB) Jul-90 BCPI Jan-90

Benchmark 5-year Jan-90 WTI Jan-90

Table 1. Data Range

A.2 Descriptive Statistics & Data Plots

Mean Median Min Max St.Dev. C.V. Skewness Ex.KurtosisComposite (6 cities) 0.49% 0.53% -1.08% 1.77% 0.47% 0.956 -0.546 4.943

Composite (11 cities) 0.50% 0.51% -1.07% 1.71% 0.45% 0.913 -0.516 5.011Calgary (AB) 0.52% 0.47% -2.72% 4.07% 1.01% 1.937 1.008 6.061

Edmonton (AB) 0.58% 0.49% -1.43% 5.21% 1.07% 1.852 1.623 7.612Ottawa-Gatineau (ON) 0.40% 0.42% -2.83% 3.60% 0.64% 1.590 -0.046 9.172

Nominal Hamilton (ON) 0.43% 0.47% -1.85% 2.22% 0.57% 1.308 -0.627 4.649Prices Halifax (NS) 0.31% 0.33% -2.13% 2.78% 0.63% 2.068 0.029 5.156

Montreal (QC) 0.32% 0.32% -2.33% 2.58% 0.52% 1.660 -0.102 6.221Quebec (QC) 0.36% 0.33% -3.36% 5.65% 0.86% 2.401 0.764 11.117Toronto (ON) 0.46% 0.50% -1.62% 2.17% 0.55% 1.203 -0.686 6.065

Vancouver (BC) 0.42% 0.38% -2.92% 3.34% 0.77% 1.814 -0.196 5.125Victoria (BC) 0.38% 0.40% -3.05% 6.38% 0.95% 2.467 0.784 8.708

Winnipeg (MB) 0.39% 0.30% -1.13% 3.19% 0.55% 1.403 0.896 5.748BCPI 0.24% 0.39% -20.31% 12.55% 4.47% 18.322 -0.649 5.389

Oil Price (WTI) 0.58% 1.00% 0.00% 1.00% 0.49% 0.853 -0.322 1.104Benchmark 5-year -0.03% -0.03% -0.79% 1.00% 0.26% -8.521 0.339 4.288

Composite (6 cities) 0.32% 0.31% -1.43% 1.68% 0.52% 1.622 -0.117 3.324Composite (11 cities) 0.33% 0.33% -1.42% 1.59% 0.51% 1.545 -0.080 3.334

Calgary (AB) 0.80% 1.00% 0.00% 1.00% 0.40% 0.496 -1.525 3.324Edmonton (AB) 0.41% 0.33% -1.63% 5.59% 1.11% 2.668 1.567 7.357

Ottawa-Gatineau (ON) 0.24% 0.24% -3.04% 3.60% 0.70% 2.870 0.211 7.625Real Hamilton (ON) 0.27% 0.35% -2.26% 1.75% 0.61% 2.235 -0.699 4.101

Prices Halifax (NS) 0.17% 0.19% -2.37% 2.69% 0.66% 3.934 -0.080 4.900Montreal (QC) 0.19% 0.18% -2.49% 2.48% 0.56% 2.878 -0.017 5.302

Quebec (QC) 0.22% 0.12% -3.72% 5.19% 0.91% 4.149 0.407 8.451Toronto (ON) 0.30% 0.33% -1.96% 2.08% 0.60% 2.006 -0.353 4.422

Vancouver (BC) 0.27% 0.22% -1.92% 3.15% 0.74% 2.711 0.270 4.101Victoria (BC) 0.21% 0.18% -2.97% 6.28% 0.98% 4.761 0.774 8.323

Winnipeg (MB) 0.27% 0.19% -1.48% 3.10% 0.59% 2.186 0.686 5.232BCPI 0.15% 0.46% -19.75% 12.00% 4.46% 28.972 -0.719 5.217

Oil Price (WTI) 0.52% 1.10% -28.00% 22.75% 7.77% 15.006 -0.402 4.061

Table 2. Nominal and Real Returns: Descriptive Statistics

16

Figure 2: Composite Index (6 Metros): Nominal vs Real

Figure 3: Composite Index (11 Metros): Nominal vs Real

17

(a) Victoria (b) Vancouver (c) Calgary

(d) Edmonton (e) Winnipeg (f) Hamilton

(g) Toronto (h) Ottawa-Gatineau (i) Montreal

(j) Quebec (k) Halifax

Figure 4: Nominal vs Real House Price Index

18

(a) West Canada-Nominal (b) East Canada-Nominal

(c) West Canada-Real (d) East Canada-Real

(e) Composite 6 Metros-Nominal (f) Composite 6 Metros-Real

Figure 5: Comparison across cities: March 1999=100

19

B Results

B.1 Lunde-Timmermann algorithm

Nominal Prices Real Pricesλ1 λ2 λ1 λ2

Composite (6 cities) 0.0094 0.0075 0.0091 0.0068Composite (11 cities) 0.0093 0.0072 0.0091 0.0063

Calgary (AB) 0.0175 0.0110 0.0178 0.0116Edmonton (AB) 0.0188 0.0098 0.0192 0.0101

Ottawa-Gatineau (ON) 0.0108 0.0101 0.0109 0.0094Hamilton (ON) 0.0101 0.0087 0.0094 0.0091

Halifax (NS) 0.0102 0.0087 0.0098 0.0092Montreal (QC) 0.0092 0.0065 0.0090 0.0069

Quebec (QC) 0.0144 0.0101 0.0145 0.0112Toronto (ON) 0.0097 0.0111 0.0095 0.0089

Vancouver (BC) 0.0129 0.0102 0.0125 0.0084Victoria (BC) 0.0157 0.0113 0.0153 0.0122

Winnipeg (MB) 0.0103 0.0052 0.0102 0.0061BCPI 0.0589 0.0681 0.0572 0.0693WTI 0.1189 0.1206 0.1040 0.1159

Benchmark 5-year 0.2000 0.2000

Table 3: LT-parameter Values

Mean Median Min Max St.Dev. C.V. Skewness Ex.KurtosisComposite (6 cities) 0.55% 0.56% -0.55% 1.77% 0.38% 0.694 0.327 1.329

Composite (11 cities) 0.57% 0.53% -0.28% 1.71% 0.36% 0.640 0.604 1.038Calgary (AB) 0.72% 0.56% -0.92% 4.07% 0.92% 1.276 1.742 3.743

Edmonton (AB) 0.87% 0.60% -0.72% 5.21% 1.00% 1.161 2.205 5.730Ottawa-Gatineau (ON) 0.49% 0.46% -0.95% 3.60% 0.55% 1.140 1.260 6.368

Bull Hamilton (ON) 0.50% 0.51% -0.78% 2.22% 0.48% 0.963 0.008 0.672Market Halifax (NS) 0.43% 0.42% -0.84% 2.78% 0.56% 1.305 0.607 2.268

Montreal (QC) 0.47% 0.41% -0.48% 2.58% 0.44% 0.928 0.929 2.316Quebec (QC) 0.62% 0.63% -0.90% 5.65% 0.79% 1.264 2.109 11.088Toronto (ON) 0.54% 0.52% -0.61% 2.17% 0.43% 0.790 0.677 2.376

Vancouver (BC) 0.70% 0.69% -0.74% 3.34% 0.62% 0.877 0.657 1.933Victoria (BC) 0.71% 0.68% -1.08% 6.38% 0.86% 1.212 1.820 9.225

Winnipeg (MB) 0.53% 0.43% -0.38% 3.19% 0.51% 0.972 1.322 3.164BCPI 1.52% 1.05% -6.09% 12.55% 3.75% 2.457 0.420 -0.099

Oil Price (WTI) 3.52% 2.88% -10.33% 48.02% 7.75% 2.204 1.285 5.366Benchmark 5-year 0.04% 0.03% -0.10% 0.48% 7.75% 2.204 1.285 5.366

Composite (6 cities) -0.48% -0.62% -1.08% 0.59% 0.53% -1.092 0.643 -0.636Composite (11 cities) -0.39% -0.57% -1.07% 0.63% 0.55% -1.394 0.547 -0.857

Calgary (AB) -0.48% -0.39% -2.72% 1.11% 0.83% -1.730 -0.217 0.460Edmonton (AB) -0.41% -0.27% -1.43% 0.91% 0.58% -1.407 0.181 -0.791

Ottawa-Gatineau (ON) -0.36% -0.43% -2.83% 0.76% 0.90% -2.490 -0.884 0.911Bear Hamilton (ON) -0.47% -0.45% -1.85% 0.94% 0.81% -1.735 0.239 -0.679

Market Halifax (NS) -0.23% -0.12% -2.13% 1.00% 0.62% -2.768 -0.712 0.789Montreal (QC) -0.14% -0.08% -2.33% 0.84% 0.48% -3.538 -1.442 4.803

Quebec (QC) -0.19% -0.11% -3.36% 1.42% 0.74% -3.886 -1.571 4.647Toronto (ON) -0.67% -0.96% -1.62% 0.74% 0.73% -1.093 0.518 -0.963

Vancouver (BC) -0.29% -0.18% -2.92% 0.88% 0.63% -2.207 -1.450 3.275Victoria (BC) -0.23% -0.19% -3.05% 1.23% 0.78% -3.434 -0.734 0.684

Winnipeg (MB) -0.07% -0.03% -1.13% 0.66% 0.38% -5.253 -0.741 0.708BCPI -2.11% -1.12% -20.31% 5.76% 4.74% -2.244 -1.297 2.049

Oil Price (WTI) -3.09% -1.57% -28.25% 11.58% 7.87% -2.547 -0.748 0.515Benchmark 5-year -0.17% -0.16% -0.79% 0.20% 0.19% -1.125 -0.513 3.189

Table 4: Descriptive Statistics, (Nominal Returns)

20

Mean Median Min Max St.Dev. C.V. Skewness Ex.KurtosisComposite (6 cities) 0.43% 0.39% -0.57% 1.68% 0.46% 1.066 0.321 0.002

Composite (11 cities) 0.43% 0.37% -0.55% 1.59% 0.45% 1.041 0.395 -0.010Calgary (AB) 0.67% 0.45% -0.73% 3.88% 0.99% 1.480 1.648 2.890

Edmonton (AB) 0.78% 0.56% -0.90% 5.59% 1.08% 1.394 1.920 4.585Ottawa-Gatineau (ON) 0.38% 0.33% -0.80% 3.60% 0.61% 1.600 1.414 4.983

Bull Hamilton (ON) 0.40% 0.44% -0.87% 1.75% 0.49% 1.224 -0.096 -0.096Market Halifax (NS) 0.33% 0.31% -0.82% 2.69% 0.57% 1.736 0.730 1.769

Montreal (QC) 0.40% 0.36% -0.66% 2.48% 0.49% 1.231 0.624 1.302Quebec (QC) 0.56% 0.47% -1.10% 5.19% 0.87% 1.555 1.468 5.670Toronto (ON) 0.44% 0.42% -0.70% 2.08% 0.49% 1.127 0.466 0.894

Vancouver (BC) 0.68% 0.60% -0.56% 3.15% 0.60% 0.882 0.880 2.004Victoria (BC) 0.75% 0.67% -1.18% 6.28% 0.92% 1.225 1.868 9.299

Winnipeg (MB) 0.47% 0.34% -0.56% 3.10% 0.56% 1.195 1.020 1.871BCPI 1.41% 1.01% -6.68% 12.00% 3.64% 2.583 0.338 -0.072

Oil Price (WTI) 3.31% 2.74% -10.50% 22.75% 6.61% 1.997 0.277 -0.108Composite (6 cities) -0.26% -0.28% -1.43% 0.75% 0.52% -2.014 0.035 -0.580

Composite (11 cities) -0.29% -0.35% -1.42% 0.80% 0.52% -1.763 0.305 -0.146Calgary (AB) -0.40% -0.37% -3.15% 1.46% 0.86% -2.122 -0.318 0.832

Edmonton (AB) -0.38% -0.30% -1.63% 0.84% 0.64% -1.693 -0.060 -0.819Ottawa-Gatineau (ON) -0.33% -0.30% -3.04% 0.83% 0.77% -2.311 -0.936 2.253

Bear Hamilton (ON) -0.38% -0.31% -2.26% 0.82% 0.73% -1.928 -0.266 -0.297Market Halifax (NS) -0.33% -0.22% -2.37% 0.91% 0.68% -2.047 -0.643 0.379

Montreal (QC) -0.19% -0.19% -2.49% 0.79% 0.47% -2.408 -1.221 4.875Quebec (QC) -0.21% -0.15% -3.72% 1.42% 0.78% -3.639 -1.416 5.030Toronto (ON) -0.29% -0.21% -1.96% 0.85% 0.65% -2.252 -0.468 -0.398

Vancouver (BC) -0.29% -0.25% -1.92% 0.91% 0.52% -1.807 -0.589 1.315Victoria (BC) -0.27% -0.22% -2.97% 1.31% 0.76% -2.778 -0.677 0.849

Winnipeg (MB) -0.13% -0.06% -1.48% 0.46% 0.40% -3.057 -1.294 2.079BCPI -2.41% -1.32% -19.75% 5.35% 4.90% -2.036 -1.139 1.362

Oil Price (WTI) -3.30% -1.60% -28.00% 10.07% 7.62% -2.305 -0.837 0.723

Table 5: Descriptive Statistics (Real Returns)

Nominal Prices Real PricesBull Market Bear Market Bull Market Bear Market

Composite (6 cities) 60.33 6.00 27.33 5.80Composite (11 cities) 59.33 5.00 27.83 4.33

Calgary (AB) 40.25 10.67 19.71 9.17Edmonton (AB) 49.67 14.67 33.25 20.00

Ottawa-Gatineau (ON) 29.17 3.00 22.29 5.29Hamilton (ON) 35.80 3.50 16.00 3.67

Halifax (NS) 20.50 3.63 20.13 4.00Montreal (QC) 35.80 2.80 22.71 4.86Quebec (QC) 24.29 2.88 14.10 4.73Toronto (ON) 44.75 4.67 17.22 4.75

Vancouver (BC) 32.00 6.60 20.67 11.50Victoria (BC) 14.11 7.33 9.36 8.18

Winnipeg (MB) 35.60 3.00 28.17 4.00BCPI 12.27 4.83 12.18 4.92WTI 13.60 5.18 10.75 4.92

Benchmark 5-year 3.97 5.47

Table 6: Bull and Bear Market Average Duration

21

(a) Victoria (b) Vancouver (c) Calgary

(d) Edmonton (e) Winnipeg (f) Hamilton

(g) Toronto (h) Ottawa-Gatineau (i) Montreal

(j) Quebec (k) Halifax

Figure 6: Bull and Bear Markets, Metros

22

(a) BCPI (b) Oil Price (WTI) (c) Benchmark 5-year

Figure 7: Bull and Bear Markets, Other

23

B.2 Synchronization Results

Cases ρ̂0 ρ− ρ+ W (ρ̂0)Panel A: n=3Vancouver, Toronto, Montreal 0.15 -0.39 0.85 1.559Ottawa-Gatineau, Montreal, Quebec 0.33 0.03 0.98 6.641Calgary, Edmonton, Winnipeg 0.21 -0.36 0.92 89.113Halifax, Ottawa-Gatineau, Quebec 0.28 -0.01 0.82 0.646Calgary, Edmonton, Oil Price 0.18 -0.11 0.89 103.266Vancouver, Toronto, BCPI 0.22 0.04 0.54 5.956

Panel B: n=4Vancouver, Calgary, Toronto, Montreal 0.19 -0.26 0.36 39.627Vancouver, Edmonton, Toronto, Montreal 0.17 -0.47 0.34 23.405Halifax, Ottawa-Gatineau, Quebec, Winnipeg 0.37 0.1 0.86 27.766Calgary, Edmonton, Winnipeg, BCPI 0.09 -0.82 0.23 94.250Calgary, Edmonton, BCPI, Oil Price 0.23 -0.24 0.46 182.521Vancouver, Toronto, Montreal, Benchmark 5-year 0.10 -0.29 0.48 24.192Halifax, Ottawa-Gatineau, Quebec, Benchmark 5-year 0.16 -0.42 0.56 28.366

Panel C: n=5Vancouver, Calgary, Toronto, Montreal, Halifax rej - - -

Table 7: Synchronization Parameter Estimates, Nominal Prices

Cases ρ̂0 ρ− ρ+ W (ρ̂0)Panel A: n=3Vancouver, Toronto, Montreal 0.17 -0.59 0.65 7.821Calgary, Edmonton, Winnipeg 0.21 -0.66 0.89 126.032Calgary, Edmonton, Oil Price 0.17 -0.56 0.99 132.762Vancouver, Toronto, BCPI 0.17 -0.34 0.52 5.752

Panel B: n=4Vancouver, Calgary, Toronto, Montreal 0.20 -0.21 0.30 55.202Halifax, Ottawa-Gatineau, Quebec, Winnipeg 0.31 -0.1 0.76 41.315Calgary, Edmonton, Winnipeg, BCPI 0.15 -0.39 0.53 131.315

Panel C: n=5Vancouver, Calgary, Toronto, Montreal, Halifax rej - - -

Table 8: Synchronization Parameter Estimates, Real Prices

24

Com

p6

Com

p11

CA

ED

GA

HA

HX

MO

QU

TO

VA

VI

WI

BC

PI

WT

IC

A5Y

µ0.938

0.927

0.834

0.776

0.905

0.930

0.807

0.740

0.676

0.930

0.716

0.652

0.770

0.649

0.563

0.421

ρij

Com

p6

0.921

0.577

0.481

0.286

0.590

0.192

0.341

-0.093

0.672

0.462

0.361

0.326

0.162

0.166

-0.024

Com

p11

0.627

0.522

0.253

0.615

0.161

0.307

-0.101

0.769

0.412

0.392

0.292

0.169

0.173

-0.026

CA

0.832

0.096

0.412

0.163

0.143

-0.117

0.466

0.213

0.330

0.130

0.168

0.051

-0.070

ED

0.042

0.330

0.157

0.090

-0.115

0.378

0.129

0.328

0.076

0.198

0.068

0.037

GA

0.391

0.363

0.460

0.389

0.185

0.336

0.261

0.639

-0.013

-0.088

-0.066

HA

0.161

0.384

-0.038

0.538

0.358

0.350

0.292

-0.007

-0.004

-0.107

HX

0.329

0.488

0.161

0.241

0.282

0.365

0.044

0.017

0.092

MO

0.276

0.230

0.090

0.180

0.590

-0.007

-0.004

0.014

QU

-0.101

0.015

0.088

0.444

0.017

-0.087

0.130

TO

0.251

0.392

0.142

0.169

0.261

0.054

VA

0.477

0.234

0.076

-0.072

-0.182

VI

0.079

0.306

0.122

0.032

WI

-0.019

-0.059

0.031

BC

PI

0.561

0.156

WT

I0.377

CA

5Y

Comp6:Composite

(6Metros),Comp11:Composite

(11Metros),C

A:Calgary,ED:Edmonton,GA:Ottawa-G

atinea

u,HA:Hamilton,HX:Halifax

MO:Montrea

l,QU:Q

ueb

ec,TO:Toronto,VA:Vanco

uver,VI:

Victoria,W

I:W

innipeg

,W

TI:

OilPrice,CA5Y:Ben

chmark

5-yea

rbond

Tab

le9:

Identi

fied

Markets

:M

ean

an

dP

air

wis

eC

orrela

tion

s(N

om

inal

Pric

es)

Com

p6

Com

p11

CA

ED

GA

HA

HX

MO

QU

TO

VA

VI

WI

BC

PI

WT

Iµ

0.850

0.870

0.715

0.695

0.810

0.835

0.759

0.658

0.565

0.810

0.579

0.471

0.665

0.673

0.579

ρij

Com

p6

0.744

0.537

0.280

0.273

0.463

-0.150

0.300

0.076

0.630

0.570

0.454

0.060

0.166

0.046

Com

p11

0.474

0.474

0.125

0.439

-0.090

0.348

-0.057

0.507

0.458

0.354

0.181

0.184

0.092

CA

0.592

0.216

0.444

-0.067

0.098

-0.146

0.350

0.374

0.335

-0.065

0.060

-0.050

ED

-0.073

0.318

0.030

0.129

-0.202

0.116

0.300

0.320

0.017

0.266

0.031

GA

0.267

0.278

0.500

0.484

0.288

0.135

0.234

0.215

-0.149

0.024

HA

-0.056

0.186

0.007

0.397

0.298

0.213

0.162

-0.059

0.005

HX

0.415

0.269

-0.117

-0.185

0.089

0.127

0.071

0.104

MO

0.246

0.180

0.084

0.280

0.402

0.081

0.141

QU

-0.003

0.270

0.292

0.450

-0.087

0.007

TO

0.315

0.220

-0.030

0.072

0.154

VA

0.731

0.247

0.129

-0.030

VI

0.249

0.276

0.196

WI

-0.077

0.038

BC

PI

0.531

WT

IComp6:Composite

(6Metros),Comp11:Composite

(11Metros),C

A:Calgary,ED:Edmonton,GA:Ottawa-G

atinea

u,HA:Hamilton,HX:Halifax

MO:Montrea

l,QU:Q

ueb

ec,TO:Toronto,VA:Vanco

uver,VI:

Victoria,W

I:W

innipeg

,W

TI:

OilPrice

Tab

le10:

Identi

fied

Markets

:M

ean

an

dP

air

wis

eC

orrela

tion

s(R

eal

Pric

es)

25