Identification of Bubble in Gold and Study of its Propagation to Equity
Markets1
Sandip Chakraborty
Vishal Jagtap
Abstract
Prior research has stipulated that financial markets all over the world are getting more
and more interconnected and the volatility in one market spills over the volatility in other
markets. The US stock market (S&P500) is claimed to be one of the most efficient equity
markets in the world. The major Asian equity markets โ Hong Kong, Singapore and India
are well influenced by S&P500 and successively by each otherโs. Traditionally gold has
been treated as hedge for the inflation; however since 2000 the volatility in the gold
prices has risen tremendously2. Identifying a bubble situation in the equity markets has
been a topic of interest for many researchers. In past decade we have seen the adverse
impact of successive shifts in bubbles in equity market. The volatility patterns in gold and
associated shifts in the conditional volatility to the dependent sensitivities from gold to
equity indices have triggered our interest to find out whether we can identify the bubble
in gold market and study its propagation to the equity markets. We have considered five
variables โ Gold price(GOLD), S&P index (SNP), Hang Seng Index(HKI), Straits Times
Index (STI) and Bombay Stock exchange index (SENSEX) for our study. We have used
Markov Switching Augmented Dickey-Fuller (MSADF) test to identify the bubble in
gold prices. To study the propagation of bubble ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก time series was constructed
after constructing a Diagonal Vector model (DVEC) of Multivariate GARCH class,
1 Second Draft Version, dated 4/6/2013 2 Gold volatility from 1995 till 2013 is shown in Figure 1.
representing the S&P500 return sensitivity with respect to the gold market. We have then
constructed three more ๐ฝ series- ๐ฝ๐ป๐พ๐ผ๐ค๐๐ก๐๐๐๐ก, ๐ฝ๐๐๐ผ๐ค๐๐ก๐๐๐ผ๐ก and ๐ฝ๐๐ธ๐๐๐ธ๐๐ค๐๐ก๐๐๐ผ๐กwhich
represented the sensitivity part over time of one marketโs return with respect to the other
market. We have the found six important sub-periods in ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐กusing Bai & Perron
(2003) methodology and analyzed each sub-period to understand the long run causality
relationship between ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐กand the other variables which represented relationship
between equity market volatility and gold market volatility. We have found that there
exist negative long run causality between the equity market return sensitivity and gold
market volatility pre financial crises; however post financial crises this relationship was
broken. The study concludes that pre-crisis situation gold accelerates the process of
bubble migration; however, post-crisis cycles are random and noisy.
Keywords: Bubble Migration, Gold, Causality, Conditional Beta, Regime Switching
I. Introduction
Numerous studies have found from empirical research that the markets all over the world
have become more interconnected over past decade. The shock or information in one
market affects the other markets. For the portfolio managers and investment practitioners
it is becoming increasing important to understand how these different markets are
interconnected. As a portfolio manager one should be aware of which market is the
largest news or shock producer and how the volatility in that market spills over the other
markets? What is the mechanism of transmission of this volatility? Is the volatility
transmitted to other markets directly or via some other markets? Is the volatility
transmission contemporaneous or non-contemporaneous? Are the relation between
markets and different financial assets which existed in past are still valid today? These
questions has been attempted to be answered using multivariate time series techniques for
modeling the volatility among different financial markets and asset classes.
The general definition of financial bubble is the phenomenon when the prices of
underlying assets rise rapidly over their intrinsic value which is mostly due to
speculation. There is no economic substance supporting such high prices. Eventually such
prices will be corrected and this is refereed as โbursting of bubbleโ. Studies of such
financial bubbles formation and burst are ever interesting topic for many economist,
researchers and policy makers. Extensive research has been done on how to identify the
bubble formation, exploring the reasons why the bubble are formed and then what
policies should one implement to avoid such bubbles. With ever interconnected markets
when such a phenomenon occurs in one market then its repercussions are felt in other
markets as well. In their recent article Philip & Yu (2011), have investigated three
financial time series โ housing price index, crude oil price, and bond prices. Their
empirical research concludes that the bubble emerged in housing market in 2002 then
traversed to selective commodity market and bond market and finally busted in 2008.
Gold is a very special asset class. Gold has proven from time to time that it is as a real
currency in times of wars and crisis. The gold has four important applications - industry,
alternative currency during uncertain times, speculative investment and central banks of
many emerging countries. Many countries are piling up the gold in their foreign reserve
to hedge against the unforeseen circumstances3. As per the article by Ghosh, et all (2004),
the demand for gold can be classified into two major categories โ โuse demandโ & โasset
demandโ. Gold is extensively used in industries such as jewelry, electronics etc. This is
the use demand of gold. The other major driver for gold as an โasset classโ is by the fund
managers. Ghosh, et al (2004), concludes that Gold is an inflation hedge in the long term
but the prices are influenced by the short run influences. We ran a univariate GARCH
model on daily gold prices (1995-2013) and found conditional variance in gold as shown
in Figure 1. We can see observe the volatility was quite high from the period of 2000 till
2012; moreover, the volatility in gold was tremendously high post 2007 subprime crises.
Figure 1 Volatility in GOLD return since 1995 to 2013.
Source : World Gold Council : http://www.gold.org/investment/statistics/
We have indentified three important markets in ASIA as key markets โ Hong Kong,
Singapore and India. The major indices in these three markets are Hang Seng Index
(HKI), Straits Times Index (STI), and SENSEX, respectively. Sariannidis et al (2009)
concluded that US equity markets (such as S&P500) are the largest news, volatility
3 Total reserves in terms of gold and US dollars can been seen from World Bank website -
http://data.worldbank.org/indicator/FI.RES.TOTL.CD
CondVGOLD
02468
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1/5
/2000
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CondVGOLD
generator and found that volatility spillover effects are significant from US markets to
Hong Kong, Singapore and India.
In this study we have first studied the volatility spillover among the major equity markets
โ SNP, HSI, STI and SENSEX along with volatility in gold spot prices (GOLD) to
understand how the volatility in one market spills over the volatility in other market. The
๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก time series constructed representing the SNP return sensitivity part over
time with respect to the gold market. Similarly, three more conditional three more ๐ฝ
series- ๐ฝ๐ป๐พ๐ผ๐ค๐๐ก๐๐๐๐ก, ๐ฝ๐๐๐ผ๐ค๐๐ก๐๐๐ผ๐ก and ๐ฝ๐๐ธ๐๐๐ธ๐๐ค๐๐ก๐๐๐ผ๐ก were constructed, which represented
the sensitivity part over time of one marketโs return with respect to the other market.
MSADF test was applied on the GOLD prices to find out different regimes in gold prices
with unit root. The structural break were found out in ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก using Bai & Perron
(2003) methodology and each sub-period was studied for understanding the long run
causality relationship between โ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก and the other conditional ๐ฝ series which
represents the propagation of bubble from gold market to the equity market.
This work contributes to the existing literature of market interconnectedness, bubble
identification and volatility migration study in following ways. Traditionally, gold is
always referred to as inflation hedge. The study first tries to identify the bubble in gold
prices and then tries to find out long run causality between equity market sensitivity over
time and gold volatility pre, post and during financial crises. The relationship between
โ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก and the other conditional ๐ฝ series would provide us useful information
about pre, post and during financial crises.
The rest of the work is arranged in following way. Section II discusses the literature
review on the market interconnectedness and methods on how to identify the bubble in
financial markets. Section III discusses the empirical approach and framework that will
be used for this study. Section IV discussed the Data analysis and empirical results.
Section V summarizes the conclusion of the study.
II. Literature Review
Analysis of volatility and modeling
The most of the financial instruments which are traded in financial markets exhibit
volatility which changes over time. The volatility represents the risk the asset carries and
modeling this risk is an important aspect of risk management. Volatility is represented by
the variance term (ฯ2) which is the square root of standard deviation (ฯ).
Traditional econometric models considered constant one period forecast variances until
the revolutionary paper published by Engle R (1982) which brought in a new
revolutionary model for modeling the time varying volatilityโ ARCH4 . The ARCH
model provided a way to study the changes in variance over the time by modeling the
variance as an autoregressive process which is related to the square of the previous error
terms in the series (Egnel, 1982). ARCH provided a systematic way to model the
variances, thus the risk factors in the time series data.
4 ARCH โ Autoregressive Conditional Heteroskedasticity
Bollerslev (1986) came up with generalized ARCH model (GARCH5). Many researches
were carried out to improve the ARCH models which gave rise to variety of flavors of
ARCH models such as Exponential GARCH or EGARCH (Nelson, 1991), NGARCH,
QGARCH etc. (Villaverde & Ramรญrez, (2010)). Bauwens, et al (2006) has summarized
the most important development in multivariate GARCH models, their specifications and
inference methods.
Globalization and market integration
Many studies have been conducted to study how the equity markets are correlated with
each other. Baele, L. (2005) studied the effect of globalization and market integration
with special focus on Western European markets. Xiao, L., & Dhesi, G. (2010) studied
volatility spillover effects across various stock indices in USA using MGARCH6 BEKK7
(Engle & Kroner, 1995) and DCC8 model (Engle 2002). Sariannidis, et al (2009) studied
volatility linkages among three Asian stock exchange markets, namely India, Singapore
and Hong Kong, during the period July 1997 to October 2005 using multivariate diagonal
BEKK GARCH model and found that all examined markets are highly integrated,
reacting to common information which was mostly derived from the USA market.
There are few studies done on the volatility spillover between oil prices, USD index, and
equity markets. Basher et al. (2011) studied the relationship between oil prices, USD
index and emerging market stock prices using SVAR (Structural Vector Autoregression)
5 GARCH โ Generalized Autoregressive Conditional Heteroskedasticity 6 MGARCH โ Multivariate GARCH 7 BEKK - Baba, Engle, Kraft and Kroner Model 8 DCC - Dynamic Conditional Correlation
model and found that emerging market stock prices get depressed if there are positive
market shocks in oil market and vice versa. Another finding of their study was increasing
stock index in emerging markets has positive spillover effect on oil markets. Sari et al.
(2010) studied volatility between four precious metals (gold, silver, platinum, palladium),
oil prices and US Euro exchange rate and found strong feedbacks in short run but weak
long run equilibrium relationship. Garefalakis et al (2011) tried to determine the effect of
equity, energy, gold, currency exchange rates on Han Seng Index using GJR-GARCH
model and found that the volatility of gold returns influence negatively to mean returns of
Han Seng index. Alom et al.(2010) studied the mean and volatility spillover effects of
food prices across different APAC markets using component GARCH method and did
not found any significant spillover effect among the APAC countries.
Prior research has stipulated that (e.g Sariannidis et al. 2009) the BEKK model would be
most suitable for running multivariate GARCH model to study volatility spillover among
various asset time return series. The mean returns equations for the BEKK model can be
written as shown in Equation 1
๐ ๐ก = ฮ + ฮฆ๐ ๐กโ1 + ๐๐ก, ๐ ๐ก = [๐1๐ก
๐2๐ก] is the vector of asset returns,
Equation 1 Mean equation for BEKK model
ฮ is the constant matrix; ๐๐ก represents the random error vector in the equation; and the
diagonal components of the matrix ฮฆ represents the lagged returns for the own variable
๐ ๐ก. The off diagonal components of the matrix ๐ต = (๐๐๐ ๐๐๐
๐๐๐ ๐๐๐) represent the mean
spillover effects across the variables under consideration. The Variance equation of the
BEKK model is shown in Equation 2 as follows:
(โ๐๐,๐ก โ๐๐,๐ก
โ๐๐,๐ก โ๐๐,๐ก) = (
๐๐๐ ๐๐๐
๐๐๐ ๐๐๐) (
๐๐๐ ๐๐๐
๐๐๐ ๐๐๐)โฒ
+ (๐๐๐ ๐๐๐
๐๐๐ ๐๐๐)โฒ
(๐๐๐,๐กโ1 ๐๐๐,๐กโ1
๐๐๐,๐กโ1 ๐๐๐,๐กโ1) (
๐๐๐,๐กโ1 ๐๐๐,๐กโ1
๐๐๐,๐กโ1 ๐๐๐,๐กโ1)โฒ
(๐๐๐ ๐๐๐
๐๐๐ ๐๐๐)
+ (๐๐๐ ๐๐๐
๐๐๐ ๐๐๐)
โฒ
(โ๐๐,๐กโ1 โ๐๐,๐กโ1
โ๐๐,๐กโ1 โ๐๐,๐กโ1)(
โ๐๐,๐กโ1 โ๐๐,๐กโ1
โ๐๐,๐กโ1 โ๐๐,๐กโ1)
โฒ
(๐๐๐ ๐๐๐
๐๐๐ ๐๐๐)
Equation 2 Volatility equation for BEKK model
In the Equation 2, matrix C is a constant matrix, matrix A represents the shocks or news
(ARCH component) and matrix B represents the past volatility affects across the markets
(GARCH term). The BEKK model was a generalized model and more specific models of
BEKK are available such as Diagonal BEKK and Scalar BEKK.
According to Leeb & Pรถtscher (2009) setting Equation 2 to B = A * D where D is a
diagonal matrix becomes
t t 1 1 t 1 1 t 2H [ | ]
t tC C A A DE A A D
Equation 3 Volatility equation for Diagonal BEKK model
The Equation 3 can model the conditional variance and covariance of the different
combinations of asset returns or time series under consideration. We have chosen
Diagonal BEKK for this study which as it resulted into better model fit.
Studies on Gold
Gold has been always treated as the inflation hedge and safe heaven in times of crises.
Ghosh, et al (2004) concludes that the gold does act as inflation hedge in long term.
Despite the importance of gold not many studies were conducted to analyze the volatility
in gold prices and its impact on other markets. Tully & Lucey (2007) applied APGARH9
model on the cash and gold future prices and found that this model was a better fit.
During the study they have found that the asymmetric component in gold was statistically
insignificant. Batten & Lucey (2009) studied the volatility in gold futures using Garman
Class Estimator and found that the gold prices are not just function of supply and demand
but are also dependent on how other inter connected markets behave. Ewing & Malik
(2012) employed univariate and bivariate GARCH models to model volatility between
gold and oil returns and found that with structural breaks in variances accounted, the
spillover effect was significant; however, ignoring the structural break the spillover effect
was not significant. Thus we can conclude that the gold prices are not just the function of
supply and demand and in more globalized world the gold volatility can affect other
markets and vice-versa.
Studies on financial bubble
There are many methods proposed by researchers on how to detect the financial bubble in
an asset. Hamilton & Whiteman (1985) proposed the methodology to detect the financial
bubble in asset by looking at the order of integration of pair of variables under
consideration. If the price of asset is rising exponentially compared to its intrinsic value
which is determined using dividends etc then one can conclude the existence of the
bubble. Hall et al. (1999) have developed the method for detecting periodically collapsing
bubbles by using Dickey-Fuller test which makes use of the Markov regime-switching
models. We will use a similar concept in identifying the bubble like situation in the gold
prices. Philip & Yu (2011) have investigated three financial time series โ housing price
9 APGARCH - asymmetric power GARCH model
index, crude oil price, and bond prices. They have used forward recursive regression
along with sequential right-sided unit root tests. Their empirical research concludes that
the bubble emerged in housing market in 2002 then traversed to selective commodity
market and bond market and finally busted in 2008.
Our approach for financial bubble detection would be to first find the regimes in gold
prices using the MSADF test. If there exist unit root in the identified Regimes then it
signifies that the gold prices during that period were not having mean reverting trend
which is very similar to a bubble like situation. The date stamping on the regimes would
help us map these bubble like situation with the equity market return sensitivity over time
using the constructed conditional ฮฒ series. Our base line conditional ฮฒ series will be
SNPwrtGOLDt . We will use method proposed by Bai & Perron (2003) to find structural
breaks in SNPwrtGOLDt . We will then work on each sub-period separately. We will run
Augmented Dickey Fuller Test for testing the unit root in the time series, Johansen
Cointegration test for testing the cointegration between the variables, VECM model to
study the long run and short run causality between the conditional ฮฒ series and finally
performing Wald Test for testing the significance and impact of the coefficients
associated with the variable. Following section briefly explains the above mentioned
terminologies.
Regime switching model and Structural breaks
Regime switching model was first proposed by Hamilton (1989). A simple regime
switching model can be modeled as
๐ ๐๐๐๐๐ 0 โถ
โ๐ฆ๐ก(๐๐ก = 0) = ๐0(๐๐ก = 0) + ๐(๐๐ก=0)0๐ฆ๐กโ1 + [โ๐พ๐โ๐ฆ๐กโ๐
๐0
๐=2
(๐๐ก = 0)] + ๐0๐ก(๐๐ก = 0)
๐ ๐๐๐๐๐ 1:
โ๐ฆ๐ก(๐๐ก = 1) = ๐1(๐๐ก = 1) + ๐(๐๐ก=1)1๐ฆ๐กโ1 + [โ๐พ๐โ๐ฆ๐กโ๐
๐1
๐=2
(๐๐ก = 1)] + ๐1๐ก(๐๐ก = 1)
๐โ๐๐๐ ๐ธ = [๐0๐ก
๐1๐ก] ~๐๐ข๐๐ก๐๐ฃ๐๐๐๐๐ก๐ ๐บ๐๐ข๐ ๐ ๐๐๐ ๐ผ๐ผ๐ท(0, [
๐0๐ก
๐1๐ก]
Equation 4 Regime Switching Model
It was method to model the non linear dynamics in the financial time series. Markov
regime switching model uses an unobserved random variable St which follows the
Markov Chain. The Markov Chain defines the transition probabilities within the defined
N states. The probabilities are defined by the equation 5.
1p|q , p,q 0,... 1[ | .]t tp P s p s q N
Equation 5 Markov Chain probabilities
The probability of moving from q state to p state is only dependent on its past state. .
Once we have obtained the Markov regimes then we will check in which regime we see
unit root behavior as per Equation 6,
๐ ๐๐๐๐๐ 0 โถ โ๐ฆ๐ก(๐๐ก = 0)๐0(๐๐ก = 0) + ๐(๐๐ก=0)0๐ฆ๐กโ1 + โ ๐พ๐โ๐ฆ๐กโ๐ ๐0๐=2 (๐๐ก = 0) +
๐0๐ก(๐๐ก = 0)
๐ ๐๐๐๐๐ 1: โ๐ฆ๐ก(๐๐ก = 1) = ๐1(๐๐ก = 1) + ๐(๐๐ก=1)1๐ฆ๐กโ1 + โ ๐พ๐โ๐ฆ๐กโ๐ ๐1๐=2 (๐๐ก = 1) +
๐1๐ก(๐๐ก = 1)
๐ผ๐ [๐(๐๐ก=0)0], [๐(๐๐ก=1)1] โ 0, โ ๐ ๐ข๐๐๐ก๐๐๐๐ก ๐๐ ๐กโ๐ ๐ก๐๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐๐๐ ๐ .
Equation 6 Unit root check
The issue with the regime switching model is that they assume fixed N states within
which the shifts will occur. Structural breaks are unexpected shifts seen in the time series.
If structural breaks are not accounted for then it will lead to inaccurate results. When
compared with the regime switching models structural break models provide better
flexibility in the sense that the number of states are assumed to be infinite10. Bai & Perron
(2003) has discussed the method of computation and analysis for finding the multiple
structural breaks in a time series. The previous methods of finding structural break were
having a major issue of limiting distribution of estimators. This issue is overcome by the
model introduced by Bai & Perron (2003) (abbreviated BP model). The primary
advantage of the BP model is that it uses effective algorithm to obtain global minimizers
of the sum of squared residuals. Secondly, the new algorithm is based on the principals of
dynamic programming and required least number of operations to find out the structural
breaks. Thirdly, the method works well for the data with pure and partial structural
breaks. Fourthly, the algorithm has inbuilt methods to construct the confidence intervals
for providing the structural breaks with date stamping. As this method overcomes the
most of the issues of previous methods of finding structural break we will also consider
this model for our study.
10 http://personal.strath.ac.uk/gary.koop/Song.pdf
We used MSADF test to find the regimes in GOLD prices and BP model for finding
structural breaks in ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก.
Augmented Dickey Fuller Test for unit root โ ADF Test
Once we have obtained the structural breaks in the data series then we will run ADF test
on the data series to see if the data series have any unit root. The ADF test is used to find
out whether the time series is stationary or exhibiting random walk behavior. The ADF
test incorporates ARMA (p,q) model with unknown order which conventional unit root
test do not. As per the article, Cheung & Lai (1995) typical ADF regression equation for
ta time series ๐๐ก can be written as shown below.
ฮ๐๐ก = ๐ + ๐พ๐ก + ๐ผ๐๐กโ1 + โ ๐ฝ๐ฮ๐๐กโ๐ + ๐๐ก๐๐=2
Equation 7 ADF Regression Equations
ADF Test Hypothesis
H0 = There is no unit root
Ha = There is unit root.
The unit root exists in the time series if we can reject the null hypothesis. Theoretically, if
there exist a unit root in the time series it means that the time series does not have mean
reverting trend. It signifies the explosive behavior in asset price.
Johansen-Juselius (JJ) Cointegration Test & VECM Model
If the variables are integrated with same order, generally of order I(1), then we can run JJ
cointegration test on these variables to see if the variables are cointegrated. The result
would be the cointegration vector with error correction term. As pointed out by Darrat &
Zhong (2002) The JJ cointegration test is preferred over the Engle-Granger test as the JJ
cointegration test allows having more than one cointegration equation. As pointed out by
Kleiman et al. (2002) the JJ test is used to determine the number of cointegrating vectors
based on following VAR or VECM model can be modeled by Equation 8 โ
ฮ๐๐ก,๐ = โฮ๐,1ฮ๐๐กโ๐,๐ + ฮ ๐๐กโ๐,๐
๐
1=1
+ ฮ๐๐ก
Equation 8 Cointegration Equation
where ฮ๐๐ก,๐ represents the conditional ๐ฝ time series matrix for our study. ฮ is the
difference operator. The Term ฮ ๐๐กโ๐,๐ is the Error correction term which represents the
long run causality relationship between the variables. The matrix can be split into two
components ๐ผ๐ฝ where the ๐ผ represents the vector error correction coefficients while the
๐ฝ represents the cointegrating equation with all the variables.
We have considered 4 conditional ฮฒ series as -๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก, ๐ฝ๐ป๐พ๐ผ๐ค๐๐ก๐๐๐๐ก
, ๐ฝ๐๐๐ผ๐ค๐๐ก๐ป๐พ๐ผ๐กand
๐ฝ๐๐ธ๐๐๐ธ๐๐ค๐๐ก๐๐๐ผ๐ก in six sub-periods. We will run the JJ test on these variables over six sub-
periods. Thus vector ฮ๐๐ก,๐ can be represented by following expression:
ฮ๐๐ก,๐ =
[ ๐ฝ๐๐๐๐ค๐๐ก๐บ๐๐ฟ๐ท๐ก
๐ฝ๐ป๐พ๐ผ๐ค๐๐ก๐๐๐๐ก
๐ฝ๐๐๐ผ๐ค๐๐ก๐ป๐พ๐ผ๐ก
๐ฝ๐๐ธ๐๐๐ธ๐๐ค๐๐ก๐๐๐ผ๐ก]
Equation 9 Cointegration test matrix
where i represents the sub-periods from 1 to 6 in our case. The JJ test provides two test
statistics โ Maximum eigenvalue test and trace test. The null and alternative hypothesis
of both the test statistics are given below
Max Eigenvalue Test Hypothesis
H0 = Number of cointegrating vectors are r
Ha = Number of cointegrating vectors are r+1
Trace Test Statistics Hypothesis
H0 = Number of cointegrating vectors are r
Ha = Number of cointegrating vectors are > r
If we found that the time series are cointegrated then we can run VECM model to find out
long run causality and short run causality between tSNPwrtGOLD and other ฮฒ series -
tHKIwrtSNP , tSTIwrtHKI ,
tSENSEXwrtSTI
The VECM model for the tSNPwrtGOLD is shown in Equation 10
(t i) (t i)
(t i) (t i) 1 1
1 1
1 1
1 1
1 1
1*
t
t t
SNPwrtGOLD i SNPwrtGOLD i HKIwrtSNP
i STIwrtH
p p
i i
KI i SENSEXwrtSTI
p p
i i
Z ECT
Equation 10 VECM Model for tSNPwrtGOLD
Similarly, the VECM model for the other conditional ฮฒ series is shown from Equation 11
to 13.
(t i) (t i)
(t i) (t i) 1 1
1 1
1 1
1 1
1 1
1*
t
t t
HKIwrtSNP i HKIwrtSNP i SNPwrtGOLD
i
p p
i i
p p
STIwrtHKI i SENSEXwrtSTi i
I Z ECT
Equation 11 VECM Model for tHKIwrtSNP
(t i) (t i)
(t i) (t i) 1 1
1 1
1 1
1 1
1 1
1*
t
t t
p p
i i
p p
i
STIwrtHKI i STIwrtHKI i SNPwrtGOLD
i HKIwrtSNP i SENSEXwrtSTIi
Z ECT
Equation 12 VECM Model for tSTIwrtHKI
(t i) (t i)
(t i) (t i) 1 1
1 1
1 1
1 1
1 1
1*
t
t t
SENSEXwrtSTI i SENSEXwrtSTI i SNPwrtGOLD
i HKIwrtSNP
p p
i i
i STIwrtHKI
p p
i i
Z ECT
Equation 13 VECM Model for tSTIwrtHKI
The 1t
ECT
term represents the long run causality relationship among the variables while
the symbols ฮฑ, , ฮณ and ฮด are the representative of coefficient of short run causality
among the variables. The term 1t is residual term in the equation. The Wald test will be
conducted on the coefficients obtained to see if together (lagged variable coefficient) they
can have long run or short run causality with the dependent variable. These coefficients
will help us to understand how the variables are related with each other.
III. Empirical Approach & Framework
Data
The variables under consideration are gold prices (GOLD), S&P500 index (SNP), Hang
Seng Index (HKI), Straits Times index (STI) and SENSEX. The daily closing prices for
each of these variables from 5th Jan 2004 till 31st Jan 2013 will be used for the study.
Framework & Approach
Our approach for financial bubble detection would be to first find the regimes in gold
prices using the MSADF test. If any of the regimes can satisfy Equation.6 then we can
conclude that we are seeing unit root in gold price. The date stamping on the regimes
would help us map these bubble like situation with the equity market return sensitivity
using the constructed conditional ฮฒ series.
The relationship between the gold and the equity markets is studied using framework
shown in Figure 2.
Figure 2 Framework of study
We have first ran the multivariate GARCH Diagonal BEKK (1,1) model on the 5
variables and find out the conditional covariance among these variables and their
individual conditional variance (representative of direct volatility of an asset). In our
case, we got 10 covariance terms and five conditional covariance terms โ one for each
variable. This has enabled us to calculate the return sensitivity of one variable with
respect to the volatility of other variable. The ฮฒ is calculated using the Equation given
below.
Step 1. Run Multivariate GARCH on daily returns data GOLD, SNP,
HKI, STI & SENSEX from 1st Jan 2004 to 31st Jan 2013
Step 2.Find Covariance among all 5 variables & conditional Variance
for each variable.
Step 3. Calculate = COV( gold,
SNP)/condVariance( GOLD)
Similary, calculate , &
Step 4. Find out structural break periods in and
arrange the , & as
per the break periods.
Step 5. For each sub period test for unit root, cointegration and obtain
VECM or VAR model. Test the coefficients.
Step 6. Analyze the results and conclude the effects with date
stamping.
(
(t t
tt
COV
Variance
Equation 14: ฮฒ formula
In step 3 we have calculated four conditional ฮฒ series - tSNPwrtGOLD ,
tHKIwrtSNP ,
tSTIwrtHKI and tSENSEXwrtSTI . The series
tSNPwrtGOLD represents the returns
sensitivity part over time of SNP market return with respect to the volatility in the GOLD
market. tHKIwrtSNP represents the return sensitivity part over time of HKI market with
respect to the volatility in SNP market. tSTIwrtHKI represents the return sensitivity over
time of STI market returns with respect to the volatility in HKI market and
tSENSEXwrtSTI represents the return sensitivity part over time of SENSEX market
returns with respect to the volatility in STI market.
tSNPwrtGOLD time series is the baseline time series and is used to study how the
volatility in gold market affects the sensitivity of returns of the worldโs largest news
producer and most efficient equity market - SNP market. We are especially interested to
find out if there are any changes in long run causality between the โother conditional ฮฒ
seriesโtHKIwrtSNP ,
tSTIwrtHKI ,tSENSEXwrtSTI and
tSNPwrtGOLD during pre or post
financial crises. For simplicity of interpretations and calculations we have considered the
volatility flow from GOLD to SNP, then SNP to HKI, then HKI to STI and then from STI
to SENSEX markets. Past studies suggest that SNP, HKI, STI and SENSEX are
interconnected.
In step 4, we have used the methodologies introduced by Bai & Perron (2003)
(abbreviated as BP Model) to estimate the structural breaks in time series. We have
applied this methodology to find structural break in the tSNPwrtGOLD . If there are n
structural breaks found in the series then we can map the series into n+1 sub-periods. The
other conditional ฮฒ series will then be mapped into these sub-periods accordingly with
date stamping. Thus, we will get 4 conditional ฮฒ time series with different sub-periods.
In step 5 and 6, we will work on each individual sub-period to find out how these
conditional ฮฒ series behave together. We will run following tests one after other to
eventually find out their long run causality relationship. We will first run ADF Test on
each conditional ฮฒ series to find out if each variable exhibit random walk phenomenon,
followed by Johansen Cointegration Test to find if they are cointegrated. If the
conditional ฮฒ series are cointegrated then we will run VECM model else VAR model to
find out long run and short run causality relationship between the other conditional ฮฒ
series andtSNPwrtGOLD . The long run causality is represented by the Error Correction
Term in VECM model and it will provide important relationship between the gold
volatility and equity market return sensitivity before, after and during financial crises.
The analysis of these sub-periods will be date matched with the unit root regimes found
in gold prices using MSADF test. This enables us to analyze the propagation of bubble
from GOLD to equity market.
IV. Data Analysis & Empirical Results
To identify bubble like situation in GOLD prices we ran MSADF test and found out
following regimes in gold prices. The two regimes are labeled as Regime0 and Regime1.
Regime 0 Regime 1
9-Dec-05 3-Jan-06 21-Jan-04 8-Dec-05
18-Apr-06 23-Aug-06 4-Jan-06 13-Apr-06
29-Aug-06 15-Sep-06 24-Aug-06 28-Aug-06
29-Sep-06 5-Oct-06 18-Sep-06 28-Sep-06
4-Jan-07 5-Jan-07 6-Oct-06 3-Jan-07
22-Feb-07 5-Mar-07 8-Jan-07 21-Feb-07
2-Nov-07 25-Jun-09 6-Mar-07 1-Nov-07
24-Jul-09 31-Jan-13 26-Jun-09 23-Jul-09
Table 1 Regimes in gold prices using Markov-Switching Augmented Dickey Fuller
test
We found that in Regime1 the gold prices were definitely having random walk
phenomenon and thus bubble like situation existed in Regim1 compared to Regime0.
Thus, we can say that we have identified Regime1 as bubble regime in gold prices. The
regimes are then sub divided into major regime periods as follows โ
Following two periods where the major Regime1 period.
1. 21-Jan-04 to 13-Apr-06 (Regime1,1)
2. 18-Sep-06 to 1-Nov-07 (Regime1,2)
Following two periods were major Regime0 period.
1. 2-Nov-07 to 25-Jun-09 (Regime0,1)
2. 24-Jul-09 to 31-Jan-13 (Regime0,2)
The empirical results for framework mentioned in Figure 2 are provided below. In Step 1,
we have run multivariate Diagonal BEKK(1,1) GARCH model on the GOLD, SNP,
HKI, STI and SENSEX . Table 1 & Table 2 summarizes ARCH and GARCH results.
ARCHGOLD ARCHSNP ARCHHKI ARCHSTI ARCHSENSEX
GOLD 0.190265 NA -0.055297 NA NA
SNP -0.032285 0.295362 -0.064055 NA NA
HKI NA 0.101171 0.163048 NA 0.044785
STI NA 0.074807 NA 0.204013 0.045883
SENSEX NA 0.099299 -0.113720 NA 0.294441
Table 2 ARCH Matrix
From Table 1 we can see that the news produced in GOLD market impacts negatively on
SNP market with coefficient of -0.032285. The news produced in SNP market does not
affect GOLD market but affects positively on SNP, HKI and SENSEX market. The news
produced in HKI markets affects negatively for both GOLD and SNP market. The news
in STI does not affect any of the market. The news produced in SENSEX does not affect
GOLD or SNP but positively affects the Asian markets.
GARCHGOLD GARCHSNP GARCHHKI GARCHSTI GARCHSENSEX
GOLD 0.972626 NA NA NA NA
SNP 0.016249 0.935787 0.040245 NA -0.014268
HKI NA 0.042454 1.003476 NA -0.017070
STI 0.010411 0.035813 0.053220 0.928660 -0.014372
SENSEX 0.021527 0.041850 0.096434 -0.080913 0.9428
Table 3 GARCH Matrix
From Table 2 we can see that the volatility in GOLD market affect SNP volatility
positively; however the volatility in SNP does not affect the GOLD but affects all other
equity market positively. The volatility in HKI has high impact on SENSEX volatility
than on STI and SNP volatility. The volatility in STI does not impact the GOLD, SNP
and HKI but does affect SENSEX negatively. The volatility in SENSEX affects
negatively on SNP, HKI and STI.
In Step 2 and 3 we have calculated the four conditional ฮฒ series - HKIwrtSNP t , STIwrtHKI t
,
SENSEXwrtSTI t and SNPwrtGOLDt
. In Step 4 we have found following structural breaks in
SNPwrtGOLDt series using BP Model.
Sub Period From To
S1 6-Jan-04 27-May-05
S2 31-May-05 5-Oct-06
S3 6-Oct-06 12-Feb-08
S4 13-Feb-08 2-Jul-09
S5 6-Jul-09 23-Nov-10
S6 24-Nov-10 31-Jan-13
Table 4 Structural breaks in SNPwrtGOLDt using BP Model
Taking this as a reference, six sub-periods from S1 to S6 were formed and all ฮฒ were then
split into six sub-periods. These four structural breaks obtained using MSADF test were
mapped onto the structural breaks obtained from the BP Model as shown in Table 5.
Gold prices
Regimes
obtained using
MSADF Test
Regime1,1 Regime1,2 Regime0,1 Regime0,2
SNPwrtGOLDt
Subperiods
using BP Model
S1 & S2 S3 S3&S4 S5&S6
Table 5 Comparison of break periods
Clearly, we can see that the regimes Regime1,1, Regime1,2 represents the pre-financial
crises period are mapped to S1, S2 and S3 sub period while the regimes Regime0,1,
Regime0,2 represents the post financial crises period and can be mapped to S3, S4, S5 &
S6 period.
The results of step5 are shown for each sub-period from S1to S6 below.
Sub-Period S1 from 6-Jan-04 to 27-May-05
Table 6 summarizes the test results conducted on S1 sub-periods.
S1 period ADF Test Does series has Unit
Root ? Johansen Cointegtration
Test
SNPwrtGOLDt
Yes
Yes with 1 cointegrated equation found
HKIwrtSNP t
Yes
STIwrtHKI t
Yes
SENSEXwrtSTI t
Yes
Table 6 Sub-period S1 - ADF, Johansen Cointegration Test results
As ADF test suggests the individual series are having unit root we can run Johansen
cointegration test. We found that the series are cointegration within S1 sub-period. We
have run VECM model and obtained the following model for 1t s
SNPwrtGOLD
1 11
1 1 1
( ) ( )
( ) ( )
1 1
1 21
0.00145 0.055 0.00204 *
0.0128 * 0.01725 * 0.249633*
s ss
s s s
t tt
t t t
SNPwrtGOLD SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI STIwrtHKID
Equation 15: Sub-period S1 tSNPwrtGOLD equation
The Error Correction Term (ECT) in the model is which represents long run causality
relationship if following.
1 1 1
1 1
( ) ( )
( )
1 1
1 1
0.00145 0.055 * 0.00204 *
0.0128 * 0.01725 *
t t
t
s
st
s s
s
t SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI
ECT
Equation 16: Error Correction Term Sub-period S1 tSNPwrtGOLD equation
In sub-period S1, we see 1t s
SNPwrtGOLD has negative long run causality with its own
lag 1 values, as well as with other conditional ฮฒ series. Also, 1t s
SNPwrtGOLD has short
run negative causality with STI return sensitivity with respect to HKI market volatility
with coefficient of -24.9%. Thus we conclude that 1t s
SNPwrtGOLD has overall
negative long run causality all equity markets in consideration.
Sub-Period S2 from 31-May-05 to 5-Oct-06
Table 7 summarizes the test results conducted on S2 sub-periods.
S2 period ADF Test Does series has Unit
Root ? Johanses Cointegtration
Test
SNPwrtGOLDt
Yes
Yes with 1 cointegrated equation found
HKIwrtSNP t
Yes
STIwrtHKI t
Yes
SENSEXwrtSTI t
Yes
Table 7 Sub-period S2 - ADF, Johansen Cointegration Test results
As ADF test suggests the individual series are having unit root we can run Johansen
cointegration test. We found that the series are cointegration within S2 sub-period. We
have run VECM model and obtained the following model for 2t s
SNPwrtGOLD
2 2 2
2 2
( 1) ( )
( 1 (
1
)1)
0.01012 0.1225 0.8713
0.00287 0.0077
s s s
s
t
s
t t
t t
SNPwrtGOLD SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI
Equation 17: Sub-period S2 tSNPwrtGOLD equation
The Error Correction Term (ECT) in the model is which represents long run causality
relationship if following.
2 2 2
2 2
1( ) ( )
( ) ( )
1
1 1
0.01012 0.1225 0.8713
0.00287 0.0077
s s s
s
t t
t t s
t SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI
ECT
Equation 18: Error Correction Term Sub-period S2 tSNPwrtGOLD equation
In period S2, we see that 2t s
SNPwrtGOLD was having negative long run causality with
its own lag 1 values, as well as with other conditional ฮฒ series. It is observed that the
coefficients of all conditional ฮฒ series has became more negative compared to S1 period.
This signifies the negative long run causality has increased over S2 period compared to
S1 period. The period S1 & S2 overlaps with the gold regime -Regime1,1 which
represents unit root. We can thus conclude that the gold could have accelerated the
process of bubble migration to the equity market.
Sub-Period S3 from 6-Oct-06 to 12-Feb-08
Table 8 summarizes the test results conducted on S3 sub-periods
S3 period ADF Test Does series has Unit
Root ? Johanses Cointegtration
Test
SNPwrtGOLDt
Yes
Yes with 1 cointegrated equation found
HKIwrtSNP t
Yes
STIwrtHKI t
Yes
SENSEXwrtSTI t
Yes
Table 8 Sub-period S3 - ADF, Johansen Cointegration Test results
As ADF test suggests the individual series are having unit root we can run Johansen
cointegration test. We found that the series are cointegration within S3 sub-period. We
have run VECM model and obtained the following model for tSNPwrtGOLD .
3 3 3
3 3
( ) 1 1
1 1
( )
( ) ( )
0.04169 0.1175 0.01947 *
0.06257 0.02607
s s s
s s
t t t
t t
SNPwrtGOLD SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI
Equation 19: Sub-period S3 tSNPwrtGOLD equation
The Error Correction Term (ECT) in the model is which represents long run causality
relationship if following.
3 3 3
3 3
1 1
1
( ) ( )
( ) ( )1
0.04169 0.1175 0.01947 *
0.06257 0.02607
t t
t
s s s
s st
t SNPwrtGOLD HKIwrtSNP
STIwrtHKI SENSEXwrtSTI
ECT
Equation 20: Error Correction Term Sub-period S3 tSNPwrtGOLD equation
In period S3, we see that 3t s
SNPwrtGOLD was having negative long run causality with
its own lag 1 values, as well as with other conditional ฮฒ series. It is observed that the
coefficients of all conditional ฮฒ series has became less negative compared to S2 period.
This was the period of sub primes crises which has affected US stock markets heavily.
The dates of major crashes in the US stock markets11 during this sub-period wereโ 27 Feb
2007, 11 Oct 2007. From the analysis of S1, S2 and S3 period we can conclude that the
long run causality was negative from equity markets to the SNP return sensitivity with
respect to gold markets. We observed the negative causality increased tremendously in S2
period and subsided in S3 period. The Regim1,2 transitioned into Regime0,1 during S3
period. From the major crash dates of US equity market we can observe that S2 period
represents the formation of bubble in financial markets.
11 Data is taken from following articles -
http://online.wsj.com/article/SB121460787893112069.html?mod=googlenews_wsj
http://www.nytimes.com/2007/03/04/business/yourmoney/04count.html?_r=2&st=cse&sq=%22Black+Mo
nday%22&scp=5&oref=slogin&
Sub-Period S4 from from 13-Feb-08 to 2-Jul-09
Table 9 summarizes the test results conducted on S4 sub-periods
S4 period ADF Test Does series has Unit
Root ? Johanses Cointegtration
Test
SNPwrtGOLDt
Yes
No Cointegration found ! HKIwrtSNP t
Yes
STIwrtHKI t
Yes
SENSEXwrtSTI t
Yes
Table 9 Sub-period S4 - ADF, Johansen Cointegration Test results
As ADF test suggests the individual series are having unit root we can run Johansen
cointegration test. Interestingly, we found that in sub-period S4 the series are no longer
cointegrated. As series are not cointegrated we can not run VECM hence we used VAR
to model the relationship between the other 3 ฮฒ series and ฮฮฒSNPwrtGOLD and found
following equation for ฮฮฒSNPwrtGOLD
4 4 4( ) ( )1 2 0.884902 * 0.057916
s s st t tSNPwrtGOLD SNPwrtGOLD SNPwrtGOLD
Equation 21: Sub-period S4 tSNPwrtGOLD equation
In Period S4, the beta series were not cointegrated yet each had unit root. The
4
stSNPwrtGOLD was only dependent on its past return sensitivity with respect to
volatility in gold market. This means that the long run causality relationship between
these beta series was broken during this period. The equity market return sensitivity with
respect to the volatility in other market is not having any long run or short run causality
with the return sensitivity of SNP with respect to the gold market volatility. This could be
termed as flight to safety phenomenon where the investors have realized that the gold
might be a safe heaven to invest in the period of financial crises.
Sub-Period S5 & S6 from 6-Jul-09 to 31-Jan2013
Table 10 summarizes the test results conducted on S5 & S6 sub-periods
S5 & S6 period ADF Test Does series has Unit
Root ? Johanses Cointegtration
Test
SNPwrtGOLDt
Yes
1 Coint eq found HKIwrtSNP t
Yes
STIwrtHKI t
Yes
SENSEXwrtSTI t
Yes
Table 10 Sub-period S5 & S6 - ADF, Johansen Cointegration Test results
As ADF test suggests the individual series are having unit root we can run Johansen
cointegration test. Interestingly, we found that in sub-period S5 & S6 there was no
significant long run causality relationship or for tSNPwrtGOLD and the other ฮฒ
series.
Few short run causality were found as below โ
For S5 sub-period
5 5
)1( 0.157387 *s st tSNPwrtGOLD SENSEXwrtSTID
Equation 22: Sub-period S5 tSNPwrtGOLD equation
For S6 sub-period
6 6 6
2( )1) ( 0.476487 * 0.345132 *s s st t tSNPwrtGOLD STIwrtHKI STIwrtHKID D
Equation 23: Sub-period S6 tSNPwrtGOLD equation
In the period S5, and S6 phenomenon of flight to safety continued and we did not observe
any long run causality between tSNPwrtGOLD with other conditional ฮฒ series. The
results suggest that from 13 Feb 2008 until Jan 2013, gold volatility has little impact on
the SNP return sensitivity and gold is treated as a different asset class.
V. Conclusion
MSADF test on gold prices revealed two regimes โ Regime0 and Regime1. Unit root was
found in Regime1 gold prices. The Regime1 was divided into two main periods โ
Regime1,1 (21-Jan-04 to 13-Apr-06) and Regime1,2 (18-Sep-06 to 1-Nov-07). Both these
periods indicate existence of bubble situation in the gold. Overall, Regime1 overlaps with
sub-period S1, S2 and S3 of tSNPwrtGOLD series. We have also observed that in S1,
S2 and S3 sub-periods all conditional ฮฒ series were cointegrated and each series had unit
root. It was found that there was a negative long run causality relationship between
tSNPwrtGOLD and other conditional ฮฒ series during these sub-periods; moreover, the
coefficients obtained from VECM equation for S1, S2 and S3 suggests that the negative
causality was at its peak in S2 sub-period compared to S1 sub-period and then it subsided
to moderate negative value in S3 sub-period. This suggests the bubble in gold market
would have migrated to the equity market during S2 period (31-May-05 to 5-Oct-06) as it
represented the peak negative causality relationship among conditional ฮฒ series.
Empirical results suggest that during sub-period S4 the conditional ฮฒ series were not
cointegrated. The relationship between conditional ฮฒ series that was broken in S4 sub-
period did not recover in S5 & S6 sub-period thus we can term S4 sub-period as โburst
periodโ and conclude that post financial crises in equity markets (represented by S4, S5
and S6 sub-periods) volatility in gold prices did not affect the return sensitivity of equity
market significantly. One reason could be โflight to safetyโ phenomenon - post financial
crises of 2007-2008 investors have realized that gold is safe heaven and treated it as a
separate asset class from equity markets. We thus conclude that pre-crisis situation gold
accelerates the process of bubble migration; however post crisis the cycles are random
and noisy.
References:
Alom, M. F., Ward, B.D, and Hu, B. (2010). Cross Country Mean and Volatility
Spillover Effects of Food Prices: Evidence for Asia and Pacific. International Review
of Business Research Papers 6(5),334-355.
Baele, L. (2005). Volatility spillover effects in European equity markets. Journal of
Financial and Quantitative Analysis, 40(02), 373-401.
Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change
models. Journal of Applied Econometrics, 18(1), 1-22.
Basher, S. A., Haug, A. A., Sadorsky, P.(2012). Oil prices, exchange rates and
emerging stock markets. Energy Economics 34 (2012), 227-240.
Batten, J. A., & Lucey, B. M. (2009). Volatility in the gold futures market.Applied
Economics Letters, 17(2), 187-190.
Bauwens, L., Laurent, S., & Rombouts, J. V. (2006). Multivariate GARCH models: a
survey. Journal of applied econometrics, 21(1), 79-109.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity.
Journal of Econometrics 31, 307-327.
Caballero, R. J., Farhi, E., & Gourinchas, P. O. (2008). Financial crash, commodity
prices and global imbalances (No. w14521). National Bureau of Economic Research.
Cheung, Y. W., & Lai, K. S. (1995). Lag order and critical values of the augmented
DickeyโFuller test. Journal of Business & Economic Statistics,13(3), 277-280.
Cheung, Y. W., & Ng, L. K. (1996). A causality-in-variance test and its application to
financial market prices. Journal of Econometrics, 72(1), 33-48.
Darrat, A. F., & Zhong, M. (2002). Permanent and Transitory Driving Forces in the
AsianโPacific Stock Markets. Financial Review, 37(1), 35-51.
Economides, N. (2001). The impact of the Internet on financial markets. Journal of
Financial Transformation, 1(1), 8-13.
Engle, R. (2002). Dynamic conditional correlation. Journal of Business & Economic
Statistics, 20(3), 339-350.
Engle, R. F., & Kroner, K. F. (1995). Multivariate simultaneous generalized
ARCH. Econometric theory, 11(01), 122-150.
Engle, R.F. (1982).Autoregressive conditional Heteroscedasticity with estimates of
the variance of United Kingdom inflation. Econometrica 50(4), 987-1007.
Ewing, B.,& Malik, F., (2012). International Review of Economics and Finance,
25(2013), 113-121.
Garefalakis, A., Dimitras, A., Koemtzopoulos, D., & Spinthiropoulos, K. (2011).
Determinant Factors of Hong Kong Stock Market. Available at SSRN 1762162.
Ghosh, D., Levin, E. J., Macmillan, P., & Wright, R. E. (2004). Gold as an inflation
hedge?. Studies in Economics and Finance, 22(1), 1-25.
Hall, S. G., Psaradakis, Z., & Sola, M. (1999). Detecting periodically collapsing
bubbles: a Markov-switching unit root test. Journal of Applied Econometrics,14(2),
143-154.
Hamilton, J. D. (1990). Analysis of time series subject to changes in regime.Journal
of econometrics, 45(1), 39-70.
Hamilton, J. D., & Herrera, A. M. (2004). Comment: oil shocks and aggregate
macroeconomic behavior: the role of monetary policy. Journal of Money, Credit and
Banking, 265-286.
Hamilton, J. D., & Whiteman, C. H. (1985). The observable implications of self-
fulfilling expectations. Journal of Monetary Economics, 16(3), 353-373.
Hammoudeh, S. M., Yuan, Y., McAleer, M., & Thompson, M. A. (2010). Precious
metalsโexchange rate volatility transmissions and hedging strategies.International
Review of Economics & Finance, 19(4), 633-647.
Hammoudeh, S., & Yuan, Y. (2008). Metal volatility in presence of oil and interest
rate shocks. Energy Economics, 30(2), 606-620.
Kleiman, R. T., Payne, J. E., & Sahu, A. P. (2002). Random walks and market
efficiency: evidence from international real estate markets. Journal of Real Estate
Research, 24(3), 279-298.
Koop, G., & Potter, S. M. (2007). Estimation and forecasting in models with multiple
breaks. The Review of Economic Studies, 74(3), 763-789.
Leduc, S., & Sill, K. (2004). A quantitative analysis of oil-price shocks, systematic
monetary policy, and economic downturns. Journal of Monetary Economics, 51(4),
781-808.
Leeb, H., & Pรถtscher, B. M. (2009). Model selection. In Handbook of Financial Time
Series (pp. 889-925). Springer Berlin Heidelberg.
Margetts, H. Z. (2012). The Internet and public policy. Policy & Internet, 1(1), 1-21.
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new
approach. Econometrica: Journal of the Econometric Society, 347-370.
Papieลผ, M., & ลmiech, S.(2012). Causality in mean and variance between returns of
crude oil and metal prices, agricultural prices and financial market prices.
Phillips, P. C., & Yu, J. (2011). Dating the timeline of financial bubbles during the
subprime crisis. Quantitative Economics, 2(3), 455-491.
Sari, R., Hammoudeh, S., & Soytas, U. (2010). Dynamics of oil price, precious metal
prices, and exchange rate. Energy Economics, 32(2), 351-362.
Sariannidis, N., Konteos, G., & Drimbetas, E. (2009). Volatility linkages among
India, Hong Kong and Singapore stock markets. International Research Journal of
Finance and Economics, 58, 141-149.
Sims, C. A., & Zha, T. (2006). Were there regime switches in US monetary
policy?. The American Economic Review, 96(1), 54-81.
Stock, J. H., & Watson, M. W. (2003). Has the business cycle changed and why?.
In NBER Macroeconomics Annual 2002, Volume 17 (pp. 159-230). MIT press.
Tully, E., & Lucey, B. M. (2007). A power GARCH examination of the gold
market. Research in International Business and Finance, 21(2), 316-325.
Villaverde, J.F., Ramรญrez, J.R.(2010). Macroeconomics and Volatility: Data, Models,
and Estimation. (Working Paper No. 16618). Cambridge, MA: National Bureau Of
Economic Research.
Xiao, L., & Dhesi, G. (2010). Volatility spillover and time-varying conditional
correlation between the European and US stock markets. Global Economy and
Finance Journal, 3(2), 148-164.