CYCLES AND COMMON CYCLES IN REAL ESTATE MARKETS
Kim Hiang LIOW, National University of Singapore
Corresponding Author
Associate Professor (Dr) Kim Hiang LIOW
Department of Real Estate
National University of Singapore
4 Architecture Drive
Singapore 117566
Tel: (65)65163420
Fax: (65)67748684
Email: rstlkh@nus.edu.sg
13 April 2006
CYCLES AND COMMON CYCLES IN REAL ESTATE MARKETS
Structured Abstract
Paper type: Research paper
Keywords: cycles, common cycles, diversification, international real estate markets
Purpose
Examines cycles and common cycles in the real estate markets of the UK, Japan, Singapore, Hong
Kong and Malaysia using a combination of time domain and frequency domain methods
Methodology / approach
Identifies the patterns of cyclical movement (if any) in the five public real estate markets; and second, to
search for common cycle characteristics and patterns in the international real estate markets. In addition
to the time domain analyzes, these empirical investigations will be further empowered by the frequency
domain method that includes spectral and co-spectral analyzes
Findings
International real estate markets are featured by cyclical behavior that exhibits phenomenal fluctuations
and that they are pro-cyclical. They do tend to move together. Furthermore, some differences in the
patterns of the common cycles and their lead-lag linkages are evident
Research implications
International investors would likely to benefit from diversifying real estate stocks across the UK and
Asia real estate markets especially in the short- and medium-term. The long-run cyclical patterns in the
real estate stock markets are however not sharply different indicating smaller diversification benefits are
to be expected in the long-run
Originality / value of the paper
Common cycle analysis advances investors’ understanding about the long–run relationship and mediumand short-term linkages across the international real estate markets, thereby allow investors and portfolio
managers an opportunity to discern any contrasting cyclical patterns at all frequencies so as to assist in
their portfolio decisions.
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CYCLES AND COMMON CYCLES IN REAL ESTATE MARKETS
Abstract
This study examines cycles and common cycles in the real estate markets of the UK, Japan, Singapore, Hong
Kong and Malaysia using a combination of time domain and frequency domain methods. We find that
international investors would likely to benefit from diversifying real estate stocks across the UK and Asia real
estate markets especially in the short- and medium-term. The long-run cyclical patterns in the real estate
stock markets are however not sharply different indicating smaller diversification benefits are to be expected
in the long-run. Common cycle analysis therefore advances our understanding about the long–run
relationship and medium- and short-term linkages across the international real estate markets.
1.
INTRODUCTION
Post-Asian financial crises have brought about a more mature and investable Asia. Essentially,
benign inflation, low interest rates, and a synchronized global recovery underway are tilting the riskreward ratio in favor of investing in Asia. Given the new wave of lucrative property investment
opportunities in the Asia-Pacific region, it is important for institutional investors to revisit and obtain
fresh insights into the risk-return performance and dynamic linkages across the various Asia-Pacific
markets from the portfolio management perspective.
Many researchers have encored the use of real estate cycle examination as a tool for making
timely property related investment decisions because property is characterized by cyclical behavior that
displays phenomenal fluctuation. According to Witkiewicz (2002), the classical view of cycles is that
they are recurrent phenomena with certain and characteristic periodicity while in the modern view, cycles
are described as coherence in many economic time-series. Additionally, Phyrr et al. (1999) define cycle
as a sine wave with certain important characteristics such as frequency, peak, trough, amplitude and
phase. These characteristics differentiate one cycle from the other. Depending on the countries’ real
estate structure and their positions along the macroeconomic cycles, investment in a portfolio of real
estate assets from certain countries may be more desirable than the others. Thus a major reason in
examining cyclical patterns in financial asset series is to ascertain if there are any common-cycles present
in a given pair of assets (Wilson and Okunuv, 1999). However, Wang (2003) notes that there is lack of
empirical research on common cycles of real estate and other sectors in the economy. In an international
context, the effectiveness of portfolio diversification in real estate also hinges on whether there are
common cycles detected across the national markets concerned, as the presence of any common cycle (s)
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will reduce the benefits of portfolio diversification. With the re-emergence of property investment
opportunities in Asia, this motivates a comprehensive study on the presence (or absence) of cycles and
common cycles across international real estate markets. Our study represents such an attempt.
This study investigates the cyclical relations between cross-market real estate stock prices over
the period 1990-2004. The five real estate markets included are Singapore, Hong Kong and Malaysia,
Japan and the UK. Given the increased significance of real estate stocks as property investment vehicles
for international investors to gain exposure into the Asia-Pacific real estate markets, this study is timely
and warranted because it will greatly enhance international investors’ understanding regarding the
strength of diversification benefits across the real estate markets. It also opens up a new avenue of
research in our continuing search for knowledge and understanding about international diversification in
real estate. Using a combination of time domain and spectral techniques, we examine the cycles and
common cyclical components across the five major real estate markets and to assess if diversification
benefits exist in investing in a portfolio that includes these real estate stocks. From a portfolio
management perspective it is important to ascertain if there are any common cycles present in the
national real estate markets since evidence of contrasting cyclical patterns would provide greater support
for a strategy to diversify across the various real estate markets.
This study therefore contributes to the international real estate literature, in particular real estate
cycle in several ways. We extend our empirical investigation to cover four major Asia and the UK real
estate markets and over an extended period of time from 1990 through 2004. This period covers the
boom and bust phases of the most recent real estate market cycle in Asia. The wider coverage of Asian
markets and time period is in line with the growing importance of Asian securitized real estate markets in
the global context in the coming years. Second, unlike earlier studies which used time domain techniques
such as correlation and cointegration, in an international setting we investigate the interdependence
between the five major real estate markets by searching for common cycles that explain the market comovements. The findings will thus provide a good opportunity for international investors to understand
the dynamics of real estate markets from a different perspective (i.e. cycles and common cycles) across
the major real estate markets and the potential portfolio implication of investing in these real estate
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stocks. This knowledge would further help fund managers in managing their exposure in Asian real
estate markets and constructing better asset allocation models. Third, in addition to the traditional time
domain method, our empirical investigations are further empowered by the frequency domain method to
achieve the research objective effectively. In particular, spectral and co-spectral analyzes are particularly
useful regarding cycles and their lead-lag linkages. On the contrary, the time domain method analyzes
aggregate statistical parameters such as mean, variance and covariance over all frequency and hence
might not be able to detect the presence of cycles and common cycles. Finally, the results of this study
should be of great interest to the US and European investors who wish to invest in Asian public real
estate markets. Evidence regarding the cross-market relationships over time will enable these investors
gain additional understanding into the potential benefits and pitfalls of portfolio diversification that
includes Asian real estate.
Our study is organized as follows. Section 2 contains a review of relevant literature. The
research methods and data sample and characteristics are described, respectively, in Sections 3 and 4.
The empirical results and implications of the findings are discussed in Sections 5 and 6 respectively. The
study is concluded in Section 7.
2.
RELATED LITERATURE
Globalization has made international diversification in real estate very important in asset
allocation and portfolio management. Starting with studies conducted on western countries, fractional cointegration analysis conducted by Wilson and Okunev (1999b) produce some evidence of co-dependence
between the US and UK securitized real estate markets but minimal co-dependence between the US and
Australia markets. This evidence leads them to support the notion of diversification across nations
though there is a need to constantly monitor the international investment climate in the wake of
important economic events such as the 1987 market correction. Their proposition is in line with Wilson
and Okunev (1996) who after using conditional mean-variance analysis to maximize return at a given
level of risk, suggest that a suitable diversification strategy by a US investor would be to have about 63%
of property investment in the US, 30% in Australia, and only 7% in UK securitized property holdings.
Cheng (1998) also produces empirical results to show that not only are the US and UK economies
5
closely related, their stock returns are also significantly positively related. Thus, it is less worthwhile for
a US investor to invest in the UK market.
Addae-Dapaah and Choo (1996)’s investigation on correlations of real stock returns from
Singapore, Malaysia, Japan, Hong Kong, UK, Australia and Canada find that with the exception of
Singapore-Malaysia markets, all the other markets exhibit a relatively low positive correlation for the
period 1977-1992. This indicates that benefits can be reaped from diversification in these markets.
However, further analysis reveals that the respective inter-country correlation coefficients are unstable.
This implies that the benefits of diversification may be less than actually calculated. Eichholtz (1997)
finds that a US real estate securities investor can derive benefit from investing in the European and Far
Eastern markets because of the low return correlations between them. By examining the correlations on
US equities indices and property indices from ten emerging markets (Argentina, China, Hong Kong,
Indonesia, Malaysia, Peru, Philippines, Singapore, Thailand and Turkey), Lu and Mei (1999) find that
investing in the emerging markets would generate certain diversification benefits because the correlation
between NAREIT and the relevant property indices is much lower than that between NAREIT and S&P
500. In addition, they find that most of the correlation coefficients between NAREIT and the emerging
markets’ property indices are actually higher in the down period as compared to the boom period.
Finally, Hu and Mei (1999)’s study on the return and risk of emerging markets also produce similar
conclusions.
More recently, Sim and Liow (2004) find that from 1990-2003, correlations between Asian
property stock markets and the US and UK are lower than that amongst Asian property stock markets.
Furthermore, Asian real estate stocks have been able to provide diversification benefits when combined
with the US/UK stock and real estate stock markets. However, the case for separate allocations to
international real estate stocks is weakened by the high correlations that are found in Asian economies
between their property stock and broader market index. Liow and Webb (2005) investigate if common
factors exist in securitized real estate markets of Hong Kong, Singapore, US and UK and the degree of
integration of the common factors with the world market using factor analysis and canonical correlation
technique. Their results indicate that there is at least one common securitized real estate market factor
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that is moderately correlated with the world real estate market and to a lesser extent, with the world stock
market.
An important observation made from the review of the real estate studies cited above is that
none of them empirically analyze the international diversification issue using the frequency domain
method. The only exception is by Wilson and Okunev (1999) who employ spectral technique to examine
the relationship between securitized property index and stock market index for evidence of cycles and
co-cycles in the USA, UK and Australia. However, they do not examine the issue of securitized property
market interdependence across the USA, UK and Australia. Our study probably represents the first to
revisit the issue of real estate stock diversification across the major Asia markets and the UK from the
cyclical perspective.
3.
RESEARCH METHODOLOGY
The principle tasks in this research are first, to identify the patterns of cyclical movement (if
any) in the five public real estate markets; and second, to search for common cycle characteristics and
patterns in the international real estate markets. In addition to the time domain analyzes, these empirical
investigations will be further empowered by the frequency domain method. A fairly extensive formal
literature has been developed on the time domain and frequency domain methods. As far as this paper is
concerned the main points are as follows.
3.1
Time Domain Methods
This refers to the usual correlation and cross-correlation analysis. However, there is a need to
detrend the series prior to conducting the analyses. Detrending, in the study of cycles, is important
because in regressing two time-series variables that are exhibiting a strong trend, a high correlation may
be observed due to the presence of the trend and not the true relationship between the two. As in business
literature, we employ the Hodrick Prescott (HP) filter to detrend the time-series before meaningful
analysis is conducted on the data. The HP-filter is chosen because it can accommodate time-series with
changing mean growth rates. Moreover, since the trend is a linear transformation of the original series
that is identical for all series considered, it is suited for comparison across many variables (Hodrick and
Prescott, 1980).
7
The use of the HP Filter has been extensive in studies of real business cycles. More specifically,
it is a smoothing method used to obtain a smooth estimate of the long-term trend component of a series.
This filter, introduced by Hodrick and Prescott (1980), is a two-sided linear filter that decomposes a
time-series, Y t, into a cyclical component, Ct and a growth component, G t.
(1)
Y t= C t+ G t
The HP procedure aims to constrain the smoothness of the growth component by setting the sum
of squares of its second-order differences less than some number. According to this filter, the trend
component, G t, of a variable, yt, is the solution to the following least square minimization problem:
T
T
t =1
t =1
Min {∑ ct2 + λ ∑ [( g t − g t −1 ) − ( g t −1 − g t − 2 )]2 }
{g t }T t = −1
(2)
Equation (2) is the Lagrange function for minimizing the sum of squares of the trend deviations,
subject to the restriction that variations in the trend component are limited. The objective function (2)
consists of two terms. The first one is a measure of fit which is minimized for Y t = G t for all t. The
second term is a measure of smoothness which becomes zero when a change in G t is constant for all t.
Thus, there is a trade-off between the two objectives of fit and smoothness and one must decide the
amount of weight to place on each goal. The weighting factor is given by λ, which is the Lagrange
multiplier, controlling the smoothness of the series. The larger the λ, the smoother the trend component
will be. Hodrick and Prescott suggest the values of λ as 100 for annual data, 1,600 for quarterly data and
14,400 for monthly data.
After the HP-filter is used to fit a smooth trend to all data series, the cyclical component of each
series can be derived. The cycle of each series can be defined as the deviations of the actual values from
the HP trend fitted to the series (Cycle = Actual Series – HP trend). Following this procedure, the
cyclical co-movement between the HP real estate stock price cycles for the five markets are examined for
their contemporaneous and cross correlations. Specifically, the correlations will reveal the degree to
which one time-series move in relation to the other whereas cross-correlations will reveal cross-market
8
linkages with regard to whether a market is pro-cyclical or counter-cyclical in relation to the other
markets. A pro-cyclical variable will tend to conform with and relate positively to the different phases of
the reference cycle while a counter-cyclical variable will move inversely to the different phases of this
cycle. Furthermore, cross-correlation analyses are conducted to establish whether a series leads, lags or is
coincident with the reference cycle. When a variable has stronger lagged (lead) correlations with the
contemporaneous values of the reference cycle, it is an indication that the former leads (lags) the latter.
Furthermore, a variable that peaks or reaches the trough before (after) the peaks or trough of the
reference cycle suggests that it is a leading (lagging) variable. A coincident relationship is observed
when the strongest correlation occurs at the contemporaneous values of the cycles
3.2
Spectral and Cross-spectral techniques
Essentially, this method is carried out in the “frequency domain”. It describes the variations in a
time series in terms of cycles of sines and cosines at different frequencies. This is portrayed in a graph
called a periodogram which provides an estimate of the amount of variance of the series accounted for by
cycles of each frequency. In our case, univariate spectral analysis is concerned with discovering price
cycles in the respective real estate markets. Bivariate cross-spectral analysis uncovers whether two the
market time series share common cycles in the relative magnitude and lead-lag pattern of cyclical
variations. Spectral method is considered to be more appropriate over the time based correlation,
regression approaches and cointegration techniques in cycle analysis not only because cycles of different
duration can be distinguished, but also because subtle relationships between the two markets at different
cycle periods can be discerned. Cross spectral analysis, which produces coherency and phase spectra,
discloses and gives estimates of the leads/lags involved between the series components that may not be
possible using time domain based methods.
In the present context, spectral analysis is first performed on all five real estate stock price series The
main intention is to decompose each series into a number of cycles sinusoidally dependent upon time via
the individual auto-covariance functions. The power of each frequency band cycle is given by the
contribution it makes to the variance of the original time series. By examining a spectrum, the important
9
bands of frequencies may be seen. Frequencies are measured in terms of cycles per month. The
frequency bands corresponding to the cycles are found to provide significant proportions of the overall
variance (Granger, 1964). In this study, the individual cyclical structures are identified by major (long)
and minor (short) cycles, and preliminary evidence of common periodicities between the respective
cycles may be obtained.
Mathematically, the spectrum of a stationary series, {Yt}, can be written as
f (ω ) =
where
1
π
∞
∑γ
k =−∞
k
e − iω k
…………………………(3)
γ k = cov(Yt , Yt − k ) , defined as the auto-covariance function of {Yt}, and ω is a real variable, the
angular frequency. It can be also expressed in the equivalent form,
f (ω ) =
1
π
∞
[γ 0 + 2 ∑ γ k cos(ωk )]
k =1
…………………………………(4)
The spectrum thus defines the relative “power” of each frequency component, i.e., its
contribution to the total variance of the whole process {Yt}. For a purely indeterminstic discrete
stationary process, the spectrum is a continuous function ofω. The total area under the curve is equivalent
to the total variance of the process, and a peak in a particular frequency range indicates the presence of a
strong cyclical component.
Second, cross-spectral analysis seeks to examine the similarities and co-movements of two time
series. Essentially, this technique performs a number of regressions between the same frequency cycles
in the two time series. The cross-spectral representation of the relationship between the two markets is
summarised at each frequency by three key statistics. The coherency spectrum estimates between the
time series measure the amount that one series can be predicted from the other at different frequencies. In
our case, it will indicate whether series A share common price cycles with series B, and the strength of
the contemporaneous relationship. Further confirmation of this evidence can be given by cross-amplitude
10
which can be interpreted as a measure of covariance between the respective frequency components in the
series. Finally, phase or phase difference gives the amount by which the frequency cycle of one series is
leading the other and is an indication of the period of time delay between the two series. The phase
spectrum will thus provide evidence on the lead-lag linkage between the two markets over time. In
addition, specific cycle frequencies that appear to share strong correlations between the two series can be
revealed.
Mathematically, the cross-spectrum of two stationary series {Xt} and {Yt} can be defined as
f xy ( ω) =
∞
∑γ
k =−∞
xy
( k )e −ikω
………………………………………(5)
where γ xy ( k ) is the cross-covariance function between the two series. This is in general a complexvalued function. It can also be written as:
f xy ( ω) = cxy ( ω) − iq xy ( ω) ……………………………………(6)
The cross-spectrum can be partitioned into a cross-amplitude spectrum
a xy ( ω) = f xy ( ω) =
cxy ( ω) + q xy ( ω)
2
2
……………………………………(7)
which describes the relationship between the magnitudes of the components in the process at different
frequencies, and a phase spectrum
ϕ xy (ω ) = tan −1 [−q (ω ) / c(ω )]………………………………………………(8)
which describes the relative phasing of the components at different frequencies. Furthermore,
C xy ( ω ) =
a xy2 ( ω )
f xx (ω ) f yy (ω )
……………………………………………(9)
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is the coherence between {Xt} and {Yt} at frequency ω. The coherence measures the squared linear
correlation between the two components of the bivariate process at frequencyω. Its value is between 0
and 1. Higher coherence values indicate stronger relationships between the two series.
4.
RESEARCH DATA
As in many previous academic real estate studies, we use returns on real estate stocks to proxy
for real estate performance. This choice is mainly justified by the availability of longer time series data
and higher frequency data (such as monthly and weekly) for real estate stocks. Whilst the adequacy of
this proxy has been extensively debated amongst real estate practitioners and researchers, it remains the
only substantive “real estate” series appropriate for any rigorous statistical analysis.
We include four major Asia real estate markets (Japan, Hong Kong, Singapore and Malaysia)
and the UK which is a world major economy and the largest European real estate market. The choice of
this Asian sample is expected to be of significant interest to the US and other international investors. The
study period is from January 1990 to September 2004 that covers the boom and bust phases of the most
recent real estate market cycle in Asia. Japan is a significantly developed economy in Asia and also a
world industrialized economy. There has been a long history of Japanese real estate companies. Other
markets like Hong Kong, Malaysia and Singapore are major economic forces in the region. Also Hong
Kong and Singapore have track record of listed real estate companies that play a relative important role
in the general stock indexes. The UK property market plays a key role in the European property markets.
Of the major institutional property markets, the global share of Japan, HK/China and the UK are about
12%, 9% and 8% respectively (UBS Warburg, 2003). Furthermore, REITs have been successfully
introduced in the five sample markets. With bullish sentiment about real estate investment opportunities
in Asia, our study reinforces the increased potential importance of Asian listed real estate in investment
portfolios for both local and international investors
We extract monthly real estate stock indexes from Datastream The FTSE 350 Real Estate,
Tokyo SE Real Estate, Hang Seng Properties, Singapore All-equity property and Kuala Lumpur SE
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properties are used to proxy, respectively, for the UK, Japan, Hong Kong, Singapore and Malaysia real
estate markets. Monthly stock return is computed as the natural logarithm of the price index relative.
5.
EMPIRICAL RESULTS
5.1
Correlation
A HP trend is fitted and removed from the time-series to obtain the cyclical component of the
five real estate stock price series. The cycle of each series can be defined as the deviations of the actual
values from the HP trend fitted to the series (Cycle = Actual Series – HP trend). The cyclical components
of the series are plotted in Figure 1 and the cyclical characteristics of the detrended series are described
in terms of their cyclical movements.
“Take in Figure 1”
A cursory inspection of the HP real estate stock price cycles reveals that the cyclical fluctuations
in Singapore, Hong Kong and Malaysia markets are quite similar. This alignment is not surprising and is
in line with the economic classification that Singapore, Hong Kong and Malaysia belong to the same
group (i.e. major tiger economies in Asia). In particular, the real estate stock price cycles of Singapore,
Hong Kong and Malaysia exhibit major troughs in 1997-1998 before peaking at the end of 1998 and
again in 1999. The major fall in the stock return cycle in 1997-1998 coincides with the period when the
financial crisis hits Asia. On the other hand, no distinctive major peaks and toughs are observed for the
UK and Japan HP real estate stock price cycles.
Table I displays the correlation matrix between the five HP real estate stock price cycles. The
lower the correlation, the greater the risk reduction benefits associated with diversification. If
international diversification in property is beneficial, a low correlation between the HP real estate price
cycles of the five markets is expected. As observed, the correlation coefficients range between 0.08
(Japan and Malaysia) and 0.74 (Singapore and HK). Moreover, 8 of the 10 correlation coefficients are
below 0.5. Clearly, the opportunities for Asian real estate stock diversification to improve portfolio
performance exist for international investors. Other observations include moderate to correlations
between the three developing real estate markets of Singapore, Hong Kong and Malaysia (correlation
coefficients range between 0.45 and 0.74), weak correlations between the UK and the three developing
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markets (correlation coefficients range between 0.28 and 0.33) and very weak correlations between Japan
and the three developing real estate markets (correlation coefficients are between 0.08 and 0.25)
“Take in Table I”
5.2
Cross-correlations between the HP real estate stock price cycles
Table II reports the cross-correlation results between the five HP real estate stock price cycles.
Up to three lead and lag cross-correlation coefficients are computed. As expected, the results show that
all real estate stock price cycles are pro-cyclical which is in accordance with a prior expectation. Hence,
international real estate price cycles have positive co-movements.
“Take in Table II”
However, there are two exceptions. The first is the cross-correlation between Malaysia and
Japan HP real estate stock price cycles. It is observed that the highest correlation between the Malaysian
and Japanese real estate price cycles happens at lag t - 1. This means that the HP Malaysian real estate
price cycle leads the Japanese real estate price cycle by a month. Similarly, Singapore HP real estate
price cycle leads the UK real estate price cycle by a month, although the correlation coefficient at lag t-1
of 0.16 (p<0.05) is smaller than the contemporaneous correlation coefficient of 0.33.
5.3
Characteristics of Real Estate Price Cycles and Common Cycles
The spectral periodograms of all five real estate market price cycles are shown in Figure 2. In
addition, Table III provides the estimated major / minor cycles and smooth periodogram values at the
respective peaks. Cyclical components are identified by the spikes or peaks in the periodogram.
“Take in Figure 2 and Table III”
The information contained in Table III provides evidence for the existence of cycles in the real
estate markets. The periodogram shows one high spike and several other smaller jagged spikes. For
Singapore and Hong Kong, the respective high peaks happen at between 29-30 months (approximately
2.5 years). The periodogram values are approximately 5.71% (Singapore) and 5.26% (Hong Kong)
which means that approximately this amount of the variation in price returns in the two real estate
markets can be accounted by the long-run cycle behavior. Using the same criterion, the results suggest
securitized real estate market major cycles of about three years (35.6 months) in Malaysia, about 3.7
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years (44 months) in both Japan and the UK. The variance at this major cycle length is about 13.11%
(Malaysia), 2.45% (Japan) and 2.69% (UK) respectively of the variance for the full period for the
individual series. Hence, the volatilities associated with the long-run cycles for the Asia developing real
estate markets (Malaysia/Singapore/Hong Kong) are much higher than those of the developed real estate
markets (Japan / UK). Additionally, at least two minor cycles each are identified for all markets. They
are, respectively, approximately at 7.7 months and 17.8 months (Singapore); 7.1 months and 19.8 months
(Hong Kong); 2.4 months and 8.1 months (Malaysia); 2.8 months, 8.5 months and 25.4 months (Japan);
and 7.1 months, 17.8 months and 25.4 months for the UK. Finally, the periodogram peaks at the 7.7
months (Singapore), 7.1 months (Hong Kong), 2.4 months (Malaysia) and 2.8 months (Japan),
respectively, report the highest of about 13.3%, 18.4%, 16.7% and 11.7%. As in Brown and Liow
(2001), this implies that shorter real estate stock price cycles display higher fluctuation than their
respective long period cycles. In short, the univariate spectral analysis has successfully picked up basis
price cyclicity within the five markets and they share a common cycle of about 2.5 - 4 years duration.
Co-spectral analysis follows to confirm this initial evidence.
The cross-spectral graphs are displayed in Figure 3. The main findings are:
“Take in Figure 3”
(a)
Singapore real estate stock price has large coherence at most frequencies with the Hong Kong
real estate stock price and is also in the same phase at these frequency bands with the latter.
Specifically, approximately 72% of the coherency values for the entire sample period are above
0.6. In addition, both coherence (0.975) and cross-amplitude values (0.03) at the Fourier
Frequency band of 0.033708 (period: 29.7 months) are the highest. This is not surprising as the
two real estate markets share the same major cycle at this frequency band. Moreover, the phase
spectra estimates at most of the frequency bands are statistically insignificant. Thus, the two real
estate markets are each closely linked with no or negligible time delays in the long run, medium
term and short run.
(b)
Singapore real estate stock price cycle is also highly linked to Malaysia real estate stock price
cycle. Specifically, the coherency values are about 0.6-0.9 at both the high and low ends of the
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Fourier frequencies. This means that if low (high) frequencies are interpreted as indicating longrun (short-run) relationships, than at least 60% of the variations in the relationship between
Singapore and Malaysia’s real estate stock prices are accounted for by the long-run and shortrun cycles. Furthermore, associated with these bands are insignificant phase values. This
evidence again suggests that the two markets move together most of the times. Again this
finding presents little surprise to international investors.
(c)
Some strong contemporaneous cyclical movements are detected between the Hong Kong and
Malaysia real estate stock prices. Specifically, strong coherency values (greater than 0.6) are
present at three pockets of frequency bands (From 17.8-178 months, 6.4-8.9 months and 2.3-2.5
months). Associated with these bands are largely insignificant phase values. This evidence again
suggests that the two Asian real estate stock markets move quite closely with each other with
negligible time differences. Nevertheless, there are other pockets of frequency bands, especially
between the 2.02-2.25 periods, where the two markets are only weakly to moderately correlated,
and with all significant phase values of up to 2.8 months. A general picture emerges is that while
the long cycle (29.7-35.6 months) relationship between the two markets is evident the shortcycle relationships in particular between the two markets are much weaker and less conclusive,
with fluctuating and inconsistent lead-lag linkages.
(d)
At low frequency bands of between 44.5 – 178 months, the coherence values between those of
Japan and Singapore, Japan and Hong Kong and Japan and Malaysia are all above 0.6.
Associated with these high correlations are weaker and smaller phase values. This implies that
the potential for diversification in the long-run is very minimal. However, high coherences fall
away as frequency bands increase. Consequently higher frequency bands display weaker and
insignificant coherences yet stronger phase values. Most of the medium and higher frequency
bands are associated with low to moderate coherence and significant phase values of between 1
– 4 months. More specifically, out of the 90 frequency bands, the number of significant phase
estimates are 39, 44 and 56, respectively, for Japan-Singapore, Japan-Hong Kong and JapanMalaysia. This evidence thus implies appropriate portfolio strategies can be devised to take
16
advantage of the phase differences between the Japanese and the Asian developing real estate
markets of Singapore, Hong Kong and Malaysia.
(e)
Co-spectral results between the UK and the Asian developing real estate markets yield mostly
weak to moderate coherency values. Specifically, the number of frequency bands that have high
coherence value (i.e. >0.6) are only 7 (UK-Malaysia), 9 (UK-Singapore) and 12 (UK-Hong
Kong). Associated with these low coherence values are pockets of frequency bands in the long-,
medium- and short-run that have significant phase values of between 1-4 months. Based on our
results, the numbers of significant phase values are 27 (UK-Singapore), 36 (UK-Hong Kong)
and 38 (UK-Malaysia) respectively. Consequently, it is again worthwhile for international
investors to pursue portfolio diversification strategies by exploiting the intertemporal linkages
between the UK and Asian markets in the short- and medium terms.
(f)
Although Japan and the UK share a common major cycle, their real estate stock price cycles are
only weakly to moderately coherent in the long- and medium- term, while incoherent in the
short-run. Again, there are small pockets of significant phase values throughout the sample
period. However, it is also observed that the lead-lag structure between the two developed real
estate markets is dynamic and the volatile phase values particularly at the short-run frequency
bands make the interpretation of the lead-lag relationships between the two markets non-trivial,
if not impossible.
6
IMPLICATIONS OF THE FINDINGS
In an international context, whether there are cycle and common cycles present in major real
estate markets is an important portfolio diversification issue. Specifically, knowledge of any co-cycle
effects among the national real estate markets will be beneficial to investors and portfolio managers in
their portfolio and tactical asset allocations decisions as the presence of common cycles is expected to
reduce the benefits of portfolio diversification. On further reflection, although much has been done on
the international real estate portfolio diversification from the traditional time domain viewpoint via
correlation and cointegration, currently very little attention has been given to the examination of common
cycles in international real estate markets from the frequency domain perspective.
17
In this study, we have identified the common cyclical characteristics and patterns in the
interactions across the major Asian and UK real estate market prices, covering the whole spectrum of
long, medium and short cycles and the phase relations. The empirical investigation is further empowered
by the frequency domain method via spectral and co-spectral analyzes which are particularly useful and
easy to understand regarding cycles and their phases. Overall, we find that international real estate
markets are featured by cyclical behavior that exhibits phenomenal fluctuations and that they are procyclical. They do tend to move together. Co-spectral analysis is employed to confirm whether there is codependence over such cycles. Some differences in the patterns of the common cycles and their lead-lag
linkages are then derived.
Among the three Asian developing real estate markets, the strongest cyclical relationship exists
between the Singapore and Hong Kong real estate markets. Specifically, Singapore real estate stock price
has large coherence at most frequencies with Hong Kong real estate stock price and is in the same phase
at these frequency bands with the latter. The two real estate markets have the same major cycle of about
2.5 years and are each closely linked with no or negligible time delays in the long run, medium term and
short run. Similarly, Singapore and Malaysian real estate stock price cycles move together most of the
times. Between Hong Kong and Malaysia, while the long cycle (29.7-35.6 months) relationship between
the two markets is evident the short-cycle relationships in particular between the two markets are much
weaker and less conclusive, with fluctuating and inconsistent lead-lag linkages. The main implication
arising from these results is that only little diversification opportunities occur among the three Asian real
estate markets especially in the long run. For Japan, its real estate stock price cycle seems to have a
larger discrepancy with the real estate stock price cycles of Singapore, Hong Kong and Malaysia, with
weak coherence and larger phase leads /lag in the medium- and short-term This finding implies
significant diversification gains may be obtained by an international investor diversifying a real estate
stock portfolio that comprises both Japanese and Malaysia/Hong Kong /Singapore real estate stocks.
Similar conclusions can be made for the UK property stock price cycles with those of Asian developing
real estate markets. Finally, the lead-lag structure between the UK and Japanese is dynamic and the
volatile phase values particularly at the short-run frequency bands make the interpretation of the lead-lag
18
relationships between the two markets non-trivial, if not impossible. There are however small pockets of
significant phase values throughout the long-, medium and short-run suggesting appropriate tactical asset
allocation strategies may be pursued.
Combining the analysis in the frequency domain and the time domain, our findings in general
support Liow et al. (2005)’ findings that investors would likely to benefit from diversifying real estate
stocks internationally in Asia and the UK especially in the short- and medium-term. However, the longrun cyclical patterns in the real estate stock markets are not sharply different suggesting possible
moderate to strong long-run cyclical co-movements across the international real estate markets. Common
cycle analysis therefore advances our understanding about the long–run relationship and short-term
linkages across the international real estate markets.
7.
CONCLUSION
This study revisits the international real estate market diversification issue from the frequency
domain perspective; such work has received little attention in the literature. The major benefit of our
methodology is that it has the ability to identify common cycle characteristics and cycles in the long,
medium and short cycles and the phase relations, thereby allow investors and portfolio managers an
opportunity to discern any contrasting cyclical patterns at all frequencies so as to assist in their portfolio
decisions. Combining the analysis in the frequency domain and time domain, this study finds that
investors would likely to benefit from diversifying real estate stocks internationally in Asia and the UK
especially in the short- and medium-term. However, the long-run cyclical patterns in the real estate stock
markets are not sharply different suggesting moderate to strong long-run cyclical co-movements across
the major international real estate markets and thereby smaller diversification benefits (if any) are to be
expected in the long-run. Common cycle analysis therefore advances our understanding about the long–
run relationship and medium- and short-term linkages across the international real estate markets. The
above findings and implications are expected to benefit practitioners as well. In an international context,
further research can employ partial coherence and three-way spectral analysis to examine the economic
interdependence and strength of inter-market relationships among the major real estate markets. It would
also be interesting to discover whether market interrelationships are stable over time using time-varying
19
spectral method. As does the current paper, future extensions have implications for international portfolio
diversification in the stock and real estate markets from a wider perspective.
Acknowledgment
The original version of this paper was presented at the 10th Asian Real Estate Society International
Conference, 18-21 July 2005, Sydney, Australia. I wish to acknowledge Ms Michelle Tee’s excellent research
assistance and the useful comments provided by the conference participants.
REFERENCES
Addae-Dapaah, K., and Choo, B. (1996). International Diversification of Property Stock – A Singaporean
Investor’s viewpoint, Real Estate Finance, 13(3), 54-66
Cheng, A. (1998). International correlation structure of financial market movements – the evidence from the
UK and the US, Applied Financial Economics 8, 1-12
Eichholtz, P. (1997). Real estate securities and common stocks: A first international look, Real Estate Finance
14(1), 70-74
Hodrick, R. and Prescott, E. (1980). Post-War US Business Cycle: An Empirical Investigation, Working
Paper, Carnegie Mellon University
Hu, J. and Mei, J. (1999). The return and risk of emerging markets, Emerging Markets Quarterly, 3(1), 10-21
Liow, K. and Sim, M. (2005). The Risk and return of Asian Real Estate Stocks, Working Paper, Department
of Real Estate, National University of Singapore
Liow, K. and Webb, J. (2005). Common Factors in International Securitized Property Markets, Working
Paper, National University of Singapore and Cleveland State University, USA
Lu, K. and Mei, J. (1999). The return distributions of property shares in emerging markets, Journal of Real
Estate Portfolio Management, 5(2), 145-160
Phyrr, S., Roulac, S. and Born, W.L. (1999), Real estate cycles and their strategic implications for investors
and portfolio managers in the global economy, Journal of Real Estate Research, 18(1), 7-68
Wang, P. (2003). A frequency domain analysis of common cycle in property and related sectors, Journal of
Real Estate, 25(3), 324-346
Wilson, P. and Okunev, J. (1996). Evidence of Segmentation in Domestic and International Property Market,
Journal of Property Finance, 7(4), 61-74
Wilson, P. and Okunev, J. (1999a). Spectral analysis of real estate and financial assets markets, Journal of
Property Investment and Finance, 17(1), 61-74
Wilson, P. and Okunev, J. (1999b). Long-term dependencies and long run non-periodic co-cycles: Real estate
and stock markets, Journal of Real Estate Research, 18(2), 257-278
Witkiewicz, W. (2002). The use of the HP-filter in constructing real estate cycle indicators, Journal of Real
Estate Research, 23(1), 65-87
20
Table I
Correlation Matrix for the HP Real Estate Stock Price Cycles
SINGAPORE
*
HONG
KONG
MALAYSIA
JAPAN
SINGAPORE
1.00
HONG KONG
0.74*
1.00
MALAYSIA
0.51*
0.45*
1.00
JAPAN
0.25*
0.12
0.08
1.00
UNITED
KINGDOM
0.33*
0.29*
0.26*
0.28*
UNITED
KINGDOM
1.00
Indicates two-tailed significance at the 5% level
Table III
Characteristics of Major and Minor Cycles of Property Stock Price Series
Major Cycle (duration:
months / periodogram
value )
Singapore
29.7 (0.0571)
Hong Kong
29.7 (0.0526)
Malaysia
35.6 (0.1311)
Japan
44.5 (0.0245)
United Kingdom
44.5 (0.0269)
Minor Cycles (months /
periodogram value)
17.8 (0.0291)
7.7 (0.1329)
19.8 (0.0511)
7.1(0.1842)
8.1 (0.1192)
2.4 (0.1669)
25.4 (0.0448)
8.5 (0.0407)
2.8 (0.1165)
25.4 (0.0171)
17.8 (0.0328)
7.1(0.0243)
Notes:
Periodogram value refers to amount of variance accounted for by the cycle of the frequency band
21
Table II
Cross-Correlation Coefficients of the HP Filtered Real Estate Stock Price Cycles
Cross Correlation with Singapore HP filtered Property Stock Price at period t
t–3
t–2
t-1
T
T+1
t+2
t+3
-0.05
-0.10
0.07
0.08
-0.02
Hong Kong
0.74*
-0.18*
-0.08
0.08
0.09
0.04
Malaysia
0.23*
0.51*
-0.21*
0.07
0.00
0.03
-0.01
-0.10
0.03
Japan
0.25*
-0.11
-0.04
-0.03
0.02
-0.07
United Kingdom
0.33*
0.16*
Cross Correlation with Hong Kong HP filtered Property Stock Price at period t
t–3
t–2
t-1
T
T+1
t+2
t+3
-0.02
0.08
0.07
-0.10
-0.05
Singapore
-0.18*
0.74*
-0.07
0.15
0.06
0.15
-0.05
-0.04
Malaysia
0.45*
0.05
0.09
0.03
0.12
-0.04
0.01
-0.02
Japan
-0.09
-0.10
0.01
0.13
-0.02
-0.09
United Kingdom
0.29*
Cross Correlation with Malaysia HP filtered Property Stock Price at period t
t–3
t–2
t-1
T
T+1
t+2
t+3
0.04
0.09
0.08
-0.08
Singapore
-0.21*
0.51*
0.23*
-0.04
-0.05
0.15
0.06
0.15
-0.07
Hong Kong
0.45*
0.03
0.00
0.06
0.08
0.05
-0.12
Japan
0.15*
-0.05
-0.02
-0.06
0.07
0.10
-0.06
United Kingdom
0.26*
Cross Correlation with Japan HP filtered Property Stock Price at period t
t–3
t–2
t-1
T
T+1
t+2
0.03
-0.10
-0.01
0.03
0.00
Singapore
0.25*
-0.02
0.01
-0.04
0.12
0.03
0.09
Hong Kong
-0.12
0.05
0.08
0.06
0.00
Malaysia
0.15*
-0.03
-0.05
-0.03
0.08
0.01
United Kingdom
0.28*
t+3
0.07
0.05
0.03
0.12
Cross Correlation with United Kingdom HP filtered Property Stock Price at period t
t–3
t–2
t-1
T
T+1
t+2
t+3
-0.07
0.02
-0.03
-0.04
-0.11
Singapore
0.16*
0.33*
-0.09
-0.02
0.13
0.01
-0.10
-0.09
Hong Kong
0.29*
-0.06
0.10
0.07
-0.06
-0.02
-0.05
Malaysia
0.26*
0.12
0.01
0.08
-0.03
-0.05
-0.03
Japan
0.28*
Notes: Sample period: Jan 1990 - Sep 2004. * - Indicates two-tailed significance at the 5% level
22
Figure 1
The HP Cycle of Real Estate Stock Price Cycles
The HP cycle of Singapore
The HP cycle of Singapore
Property
PropertyStock
StockReturn
Prices
The HP cycle of Hong Kong
Property Stock Prices
Return
0.60
0.40
0.6
0.4
0.20
0.00
-0.20
0.2
0
-0.2
-0.40
-0.60
-0.4
-0.6
Period (Mths)
Period (Mths)
The HP cycle of Malaysia
The HP cycle of Malaysia
Property
Stock
Property
StockReturn
Prices
0.8
The
TheHP
HPcycle
cycleof
ofJapan
Japan
PropertyStock
StockReturn
Prices
Property
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
0.6
0.4
0.2
0
-0.2
-0.4
Period (Mths)
Period (Mths)
TheHP
HPcycle
cycleofofUnited
UnitedKingdom
Kingdom
The
Property
Stock
Prices
Property
Stock
Return
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
Period (Mths)
23
Figure 2
Spectral Results of Real Estate Stock Price Series
Spectral analysis: Spore Property Stock Return
Spectral analysis: Japan Property Stock Return
No. of cases: 178
0.14
0.12
0.12
0.10
0.10
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.00
0
20
40
60
80
100
120
140
160
0.12
0.12
0.10
0.10
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0.02
0.00
180
0.00
Periodogram Values
Periodogram Values
No. of cases: 178
0.14
0
20
40
60
80
Period
120
140
160
0.00
180
Spectral analysis: United Kingdom Property Stock Return
Spectral analysis: Hong Kong Porperty Stock Return
No. of cases: 178
No. of cases: 178
0.20
0.20
0.04
0.04
0.15
0.15
0.03
0.03
0.10
0.10
0.02
0.02
0.05
0.05
0.01
0.01
0.00
180
0.00
0.00
0
20
40
60
80
100
120
140
160
Periodogram Values
Periodogram Values
100
Period
0
20
40
60
80
100
120
140
160
0.00
180
Period
Period
Spectral analysis: Malaysia Property Stock Return
Periodogram Values
No. of cases: 178
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0
20
40
60
80
100
120
140
160
0.00
180
Period
24
Figure 3
Squared Coherency
X:Spore Property Stock Return Y:Hong Kong Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
X:Spore Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
20
40
60
80
100
120
140
160
0.0
180
Squared Coherency
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
180
0
20
40
60
80
100
120
140
160
X:Spore Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Squared Coherency
1.0
Squared Coherency
Squared Coherency
1.0
0
Cross-Spectral Results
Squared Coherency
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
Period
Period
20
40
60
80
100
120
140
160
0.0
180
Period
Cross Amplitude
X:Spore Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.07
0.08
0.08
0.06
0.06
0.07
0.07
0.05
0.05
0.06
0.06
0.05
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0.00
20
40
60
80
100
120
140
160
0.00
0.00
180
0
20
40
60
80
Period
100
120
140
160
Phase Spectrum
X:Spore Property Stock Return Y:Hong Kong Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
2.0
2.0
1.5
1.5
1.0
1.0
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
180
40
60
80
100
Period
0.03
0.03
0.02
0.02
0.01
0.01
0.00
0.00
180
0
20
40
60
80
120
140
160
140
Phase Spectrum
X:Spore Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0
-1
4
2
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-1
-2
-2
-3
-3
-3
-4
-4
180
-4
60
80
100
Period
0.00
180
4
0
40
160
3
1
20
120
Phase Spectrum
1
0
100
X:Spore Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
2
Phase Spectrum
Phase Spectrum
0.5
20
0.04
Period
3
0
0.04
Period
Phase Spectrum
0
Cross Amplitude
Cross Amplitude
X:Spore Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.07
Cross Amplitude
Cross Amplitude
Cross Amplitude
X:Spore Property Stock Return Y:Hong Kong Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
120
140
160
0
20
40
60
80
100
120
140
160
-4
180
Period
25
Squared Coherency
X:Hong Kong Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
40
60
80
100
120
140
160
1.0
1.0
1.0
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.0
180
0.0
0.0
0.0
180
0
20
40
60
80
Cross Amplitude
X:Spore Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.020
0.015
0.015
0.010
0.010
0.005
0.005
0.000
20
40
60
80
100
120
140
160
0.000
180
0.06
60
80
0.05
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
20
40
60
80
1
1
0
0
-1
-1
-2
-2
-3
100
120
140
160
-3
180
100
120
140
160
0.0
180
100
120
140
160
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0.00
0.00
180
0
20
40
60
80
100
120
140
160
0.00
180
Period
Phase Spectrum
X:Hong Kong Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Phase Spectrum
X:Hong Kong Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
3
2
Period
40
Cross Amplitude
X:Hong Kong Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.07
0
3
2
Phase Spectrum
Phase Spectrum
2
80
20
Period
0.00
3
60
0
Period
3
40
160
0.06
Phase Spectrum
X:Spore Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
20
140
0.07
Period
0
120
Cross Amplitude
X:Hong Kong Property Stock Return Y:Malaysia Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Cross Amplitude
Cross Amplitude
0.020
0
100
Period
Period
Cross Amplitude
20
1.0
2
1
1
0
0
-1
-1
-2
Phase Spectrum
0
Squared Coherency
X:Hong Kong Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Squared Coherency
0.8
Squared Coherency
Squared Coherency
Squared Coherency
X:Spore Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-2
-3
0
20
40
60
80
100
Period
120
140
160
-3
180
-4
0
20
40
60
80
100
120
140
160
-4
180
Period
26
Squared Coherency
X:Malaysia Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Squared Coherency
X:Hong Kong Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
1.0
0.8
0.6
0.6
0.4
0.4
0.2
Squared Coherency
0.2
0.0
20
40
60
80
100
120
140
160
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.0
0.0
180
0.0
0.0
180
0
20
40
60
80
0.030
0.030
0.025
0.025
0.020
0.020
0.015
0.015
0.010
0.010
0.005
0.005
0.000
0.000
180
20
40
60
80
100
120
140
160
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-4
100
Period
40
60
80
0.03
0.02
0.02
0.01
0.01
0.00
0.00
180
20
40
60
80
120
140
160
100
120
140
160
2
1
0.030
0.030
0.025
0.025
0.020
0.020
0.015
0.015
0.010
0.010
0.005
0.005
20
0
40
60
80
0
140
160
0.000
180
4
3
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-1
-1
-3
-2
-2
-4
180
-3
-3
180
100
Period
120
4
0
80
100
4
1
60
160
0.000
2
40
140
Phase Spectrum
X:Malaysia Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
3
20
120
Period
4
0
100
Cross Amplitude
X:Malaysia Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.03
0
Phase Spectrum
Phase Spectrum
4
80
20
Period
Phase Spectrum
X:Malaysia Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
3
60
0
Period
4
40
160
0.04
Phase Spectrum
X:Hong Kong Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
20
140
0.04
Period
0
120
Cross Amplitude
X:Malaysia Property Stock Return Y:Japan Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
Cross Amplitude
Cross Amplitude
Cross Amplitude
X:Hong Kong Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0
100
Period
Period
Cross Amplitude
0
0.0
180
0.9
0.8
120
140
160
Phase Spectrum
Squared Coherency
0.8
0.9
Squared Coherency
1.0
Squared Coherency
X:Malaysia Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
-4
0
20
40
60
80
100
120
140
160
-4
180
Period
27
Squared Coherency
Squared Coherency
X:Japan Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
20
40
60
80
100
120
140
160
0.0
180
Period
Cross Amplitude
Cross Amplitude
X:Japan Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
0.018
0.018
0.016
0.016
0.014
0.014
0.012
0.012
0.010
0.010
0.008
0.008
0.006
0.006
0.004
0.004
0.002
0.002
0.000
0
20
40
60
80
100
120
140
160
0.000
180
Period
Phase Spectrum
Phase Spectrum
X:Japan Property Stock Return Y:United Kingdom Property Stock Return
No. of cases: 178
User-defined weights:.0357 .2411 .4464 .2411 .0357
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
0
20
40
60
80
100
120
140
160
-3
180
Period
28
29