Proceedings of the 2nd IMT-GT Regional Conference on Mathematics, Statistics and Applications
Universiti Sains Malaysia, Penang, June 13-15, 2006
CAUSAL RELATIONSHIP BETWEEN STOCK PRICE AND MACROECONOMIC
VARIABLES IN MALAYSIA
Cheah Lee Hen 1 , Zainudin Arsad 2 , Husna Hasan 3
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.
Abstract: Financial markets are interrelated and increasingly global. When making decisions,
traders incorporate information pertaining to price movements and volatility in the asset they
are trading. Thus, understanding how markets influence one another is important for pricing,
hedging and regulatory policy. This study makes use of Kalman filter and variety of ARCH-
type models to investigate the feedback causal relationship between stock prices with each of
currency exchange and derivative product. Since the development by Kalman and Bucy in
1960s, Kalman filter technique has been the subject of extensive research and application. It is
a set of equations which allows an estimator to be updated once a new observation becomes
available. Three series used are monthly Kuala Lumpur Composite Index (KLCI), Pound
Sterling (STL) and Kuala Lumpur Composite Index Futures (FKLI). All data covered from
January 1997 to February 2005. In general, the results show that dynamic linkages between
stock market and derivative are relatively weak. For the asymmetry GARCH models, there is a
bi-directional causality runs between KLCI and FKLI. On the other hand, the symmetry
GARCH models fail to reveal any recognizable pattern between the two variables. For the
dynamic between KLCI and STL, the results suggest that many of the relationships or effects
between the two series are significant. However, only KF-GARCH-M model has a bi-
directional feedback effect between KLCI and STL. In addition, the result proves the existence
of leverage effect in the stock market. However, the there is no evidence of risk-return trade-
off in the Malaysian stock market.
Keywords: Kalman filter, GARCH, stock market, currency exchange
1. Introduction and Literature Review
Establishing the lead-lag relationship between stock prices and macroeconomic
variables is important. By knowing these relationship, investors can earn profits by exploiting
past information of the variables. In addition, they may be used as indicator to formulate
current economic stabilization policies. Therefore, the issues of whether stock prices and
macroeconomic variables are related or not have received considerable attention. Many works
have been done for past few decades to examine the relationship between stock prices and
financial futures as well as the currency exchange. However, there is no empirical or theoretical
consensus on the issue of whether these variables are related and the direction of causation if
they are related. This paper provides further empirical evidence on the above issue. The
relationship between Kuala Lumpur Composite Index (KLCI), Pound Sterling (STL) and
Composite Index Futures (FKLI) are investigated using the Kalman filter technique (KF) and
Generalised Autoregressive Conditional Heteroskedasticity (GARCH).
Arsad et. al. (2004) (see Reference ) found that foreign currency and interest rate
significantly affect the stock prices. In addition, there is a negative relationship between the stock
prices and money supply. Mansor (1999) (see Reference ) investigated the dynamic between
seven macroeconomics and the Malaysian stock prices using cointegration and Granger-causality
tests. The results show that changes in the official reserves and exchange rates affect the KLCI.
Mukesh et. al. (1996) (see Reference ) examined co-movement in the Japanese Yen,
Australian Dollar, Singapore Dollar, Malaysian Ringgit and New Zealand Dollar exchange rates.
The Vector Autoregressive (VAR) model is used to investigate the channels of influence among
these currencies. In addition, analyses are carried out to investigate the changes of these channels
over two important currency-coordinating agreements, namely the Louvre Accord and Plaza
There are many other studies that have investigated the lead-lag relationship between
futures market and cash market. Those papers including Lim (1992) (see Reference ) who
found that there is no lead lag relationship between the Nikkei Stock Average (NSA) stock and
futures markets. Wong and Meera (2001) (see Reference ) studied the market efficiency
between KLCI and FKLI by using Granger causality and error correction approaches. The data
are divided into two sub-samples: before financial crisis, January 1996 to March 1997 and during
the financial crisis, April 1997 to September 1998. The results show that KLCI price lead the
stock index futures market before the economic crisis but not vice versa. In addition, there is no
long run equilibrium relationship between both markets. Chan and Karim (2004) (see Reference
) analyse the lead lag relationship between spot and futures market of the KLCI. They used
cointegration and error-correction model in their analysis. Daily closing price from January 1996
to December 2002 is used. It is suggested that KLCI price and the corresponding futures markets
are cointegrated. Also, it is proven that futures prices can be a good indicator on predicting spot
prices due to the stronger impacts of futures prices on cash markets compared to that from cash
market to futures market.
The paper is organized as follows: Section two discusses empirical methodology and
data, while Section three presents empirical results. In Section four concluding remarks is
2. Data and Methodology
One of the methodologies used in this study is Kalman filter (KF). The existence of
Kalman filter is due to the work by Kalman and Bucy in 1960. It is an algorithm for sequentially
updating a linear projection for the system. This algorithm consists of recursions estimating the
parameter vector before a new observation becomes available, forecasting this observation and
updating the state vector once the new observation is available. Details of this method can be
found in Harvey (1981) (see Reference ). State-space representation of the model can be
xt = αθt + εtx (2.1)
θt = βθt −1 + Sεtθ (2.2)
εtx ~ i.i.d .N (0, C ), εtθ ~ i.i.d .N (0, Q), E (εty εtθ ) = 0.
where Equation (2.1) and Equation (2.2) are the measurement equation and transition equation
respectively. xt and θt are n × 1 vector of observed variables and m × 1 vector of unobserved state
variables at time t respectively. The system matrices α, β and S are matrices of parameters of
dimension (n × m), (m × m) and (m × r ) respectively. The matrices C and Q are assumed to be
constant. Once the model is written in state-space form, parameters estimates can be obtained by
maximum likelihood function, where the Kalman filter is used to update the unobserved
components. The Kalman filter algorithm is given as follows:
θt|t −1 = μ + βθt −1|t −1
Pt|t −1 = βPt −1|t −1 β ' + Q (2.4)
ηt|t −1 = xt − xt |t −1 = xt − αθt|t −1
ft|t −1 = αPt −1|t −1α ' + C (2.6)
θt|t = θt −1|t −1 + K t ηt|t −1 (2.7)
Pt|t = Pt −1|t −1 − Kt αPt|t −1 (2.8)
where Kt = Pt −1|t −1α ' ft'|t −1 is the Kalman gain, which determine the weight assigned to new
information about θt contained in the prediction error. θt|t −1 is the one-step-ahead estimate of the
state vector and Pt|t −1 is the corresponding mean squared error (MSE). Equation(2.5) is the
prediction error. Its corresponding MSE is given by Equation(2.6), Equation(2.7) and Equation
(2.8) are the updating equations after incorporating the new information supplied by xt .
The algorithm of Kalman filter can be used to construct the likelihood function which will be
used for numerical computation of the parameters. The likelihood function can be written as:
1 N 1 N ' −1
log Lα − ∑ log | ft | − ∑ ηt ft ηt (2.9)
2 t =1 2 t =1
where f t = αPt|t −1α ' + C and ηt|t −1 = xt − xt|t −1 = xt − αθt|t −1 is the prediction error. Equation (2.9) is
also known as the prediction error decomposition form of the likelihood.
In this paper, state-space models with conditional heteroskedasticity will also be
considered. Engle (1982) (see Reference ) introduced the Autorgressive Conditional
Heteroscedasticity (ARCH) model to cope with changing variance. Bollerslev (1986) (see
Reference ) proposed a Generalized ARCH (GARCH) model which has a more flexible lag
structure, modeling the error variance as an Autoregressive Moving Average (ARMA) process.
Over the years extension to the GARCH model have been developed by Engle et. al. (1987) (see
Reference ), Glosten et. al (1993) (see Reference ) and Nelson (1991) (see Reference )
(GARCH-M, TARCH and EGARCH respectively). The use of ARCH-type models for modelling
and predicting volatility is now very common in finance. A typical finding is that these models
provide superior forecasts of volatility than those which simply assume homoscedasticity of the
The state-space model with ARCH disturbances as proposed by Harvey, Ruiz and Sentana (1992)
(see Reference ) is given as:
xt = αθt + εt* (2.10)
θt = βθt −1 + Sεtθ (2.11)
εt* ~ N (0, ht ) (2.12)
and ht is assumed to follow various ARCH-type equations as given below:
ARCH(1): ht = β0 + β1εt2−1 (2.13)
GARCH(1,1): ht = β0 + β1εt2−1 + β2 ht −1 (2.14)
GARCH(1,1)-M: xt = αθt + γht + εt*
ht = β0 + β1εt2−1 + β2 ht −1 (2.15)
Threshold-ARCH: ht = δ0 + δ1εt2−1 + δ2 εt2−1D + δ3 ht −1 (2.16)
εt −1 εt −1
Exponential-GARCH: ln ht = λ0 + λ1 + λ2 + λ3 ln ht −1 (2.17)
ht −1 ht −1
The conditional volatility equations shown by Equation (2.16) and Equation (2.17)
differentiate between positive and negative shocks in term of the magnitudes of their impacts on
the future volatility of asset returns. Equation (2.16) models the asymmetry (measured by δ2 ) in
the stock price volatility reaction to information shocks by utilizing dummy variables, while
Equation (2.17) models the leverage effect (measured by λ2 ) to be exponential. It is a common
finding in the finance literature that bad news ( εt −1 < 0 ) has a larger impact on the future volatility
of asset returns than good news ( εt −1 > 0 ).
The monthly data of Kuala Lumpur Composite Index (KLCI) and Kuala Lumpur
Composite Index Futures (FKLI) are used as proxy to the movement of stock prices for overall
market and to represent the overall market futures respectively. The KLCI was introduced in
1986 and it consists of some Malaysia’s largest publicly corporations. Note that the KLCI series
is the underlying instrument of the FKLI, the financial future contracts traded in Malaysia
Derivatives Exchange (MDEX). The exchange rate is represented by one of the world's most
widely traded currencies, STL. The UK has the fifth largest economy in the world and the second
largest in Europe. Its capital, London is one of the largest financial center in the world. Therefore,
it is believed that the UK’s economy is associated with many other capitalist economies in the
world. The three series are collected from January 1997 to February 2005 and they are
transformed into returns to obtain the stationary series, using the formula as below:
Rt = log( Pt / Pt −1 ) *100 (2.18)
where Rt is the returns, Pt is the price at last trading day on month t.
3. Results and Discussion
Column two and three in Table 1 shows the estimated parameter of the Kalman filter
models relating KLCI & STL and KLCI & FKLI respectively. The numbers in the parathesis are
standard errors which are calculated numerically. The results show that there is only one
significant relationship from the KLCI & STL model, whereby the estimate of α3 is significant at
1% level (-0.1130). This result suggests that STL at current month is significantly affected by last
month’s KLCI price at 1% level. The negative sign of α3 indicates that domestic stock prices
have negative effects on exchange rates, implying that a past increase of stock prices appreciates
domestic currency (i.e. decreasing exchange rate). For KLCI & FKLI model, the results suggest
that many of the feedback effects between the two series are not significant. The results suggest
the existence of other variables that may affect the KLCI. From Table 1, it is known that most of
the parameters in matrix S are statistically significant from zero. The higher value of S12 for the
KLCI & FKLI model indicates the higher correlation between noise of KLCI and FKLI for the
model as compared to that from the KLCI & STL model. Note that magnitudes of S11 are larger
than the magnitudes of S22 for KLCI & STL model, indicating that the KLCI market is noisier
than the STL market. However, the opposite occurrence is found form the KLCI & FKLI model.
Table 2 shows the dynamic between KLCI and STL series. The results show that KF-
EGARCH has the highest log likelihood value (-396.6206) among the tabulated models. This
result coincides as the smallest values of both AIC and BIC (813.2412 and 837.9003). From
Table 2, most of the parameters are significantly different from zero. Therefore, the results
suggest that many of the feedback effects between the two series are significant. Note that the
autoregressive coefficient α1 and α4 are both significant at the 1% level for all models. This
shows that both the KLCI and STL are dependent on observations in the previous month. In
addition, the results show that α2 from KF-GARCH, KF-GARCH-M, KF-EGARCH and KF-
TARCH are significant, indicating that KLCI series is influenced by STL series (4.9388, 4.9758,
3.4791 and 2.5643 respectively). The positive coefficient implies that past increases of exchange
rate have long-run positive effects on asset prices, increasing stock prices in KLCI. The positive
effects of exchange rate in stock prices imply that depreciation of domestic currency boosts asset
prices because domestic assets become more attractive to foreign investors and thus increase the
profits of exporting firms.
From Table 2, it can be seen that α3 is also significantly different from zero for KF-
ARCH and KF-GARCH-M models. The result indicates that current value of STL is affected by
the last value of KLCI price (0.0686 and -0.1222). This result is similar to that found in pure KF
model. The negative sign of α3 suggests that domestic stock prices have negative effects on
exchange rates, implying that a past increase of stock prices appreciates domestic currency. From
Table 2, note that only KF-GARCH-M model has a bi-directional feedback effect between KLCI
and STL. However, the coefficient on the expected risk, γ is not statistically significant (0.0107).
Results from analyses also show that both parameter of leverage effect significant at 1% level in
KF-EGARCH and KF-TARCH models. From Table 2, it is also noted that almost all parameters
in covariance matrices of S are significant at 1% level.
Table 1: Dynamic between KLCI and exchange rates
Parameter KLCI & STL KLCI & FKLI
Log L -427.83 -233.99
AIC 869.66 418.98
BIC 886.92 499.24
α1 0.2056 0.1019
α2 0.1634 0.0820
α3 -0.1130 0.6161
α4 -0.1579 -0.4348
S11 9.5750 0.5394
S12 -1.9050 9.7854
S22 5.2510 9.8022
Note: *** denotes significant at 1% level.
Table 3 shows the dynamic between KLCI and FKLI series. The results show that KF-
GARCH-M has the highest log likelihood value (-207.5728). The KF-GARCH-M model also
ranks the second small of both AIC and BIC among the tabulated models. It can be seen from
Table 3 that the asymmetry GARCH-type model has significant parameters at the Ω structure.
For KF-EGARCH model, it is shown that α3 significantly different from zero at 1% level. The
result indicates that the previous value of KLCI has significant effect on the FKLI. In other
words, there is a uni-directional relationship running from stock market to futures market. This
shows that trading of FKLI very much rely on the movement of its underlying asset, KLCI. This
is due to the fact that traders will look upon the movement of KLCI to anticipate future
movement of FKLI price.
For KF-TARCH model, however, there is a bi-directional causality runs between KLCI
and FKLI. The causal effect from futures prices to stock prices is found to be stronger (2.8975 as
compared to 2.0218) than that from stock market to future market. Stoll and Whaley (1990) (see
Reference ) interpret this evidence as meaning that futures market reflects new information
more quickly than the stock market. According to Chan (1991) (see Reference ), since firm
specific information is diversifiable and market-wide information is systematic, the discovery of
market wide information is more important, so he hypothesized that the feedback from the futures
market into the stock market is larger than the reverse. On the other hand, the symmetry ARCH –
type models fail to reveal any recognizable patterns between KLCI and FKLI series.
Table 2: Dynamic between KLCI and STL for Kalman filter-ARCH-type models
KF-ARCH KF-GARCH KF-GARCH-M KF-EGARCH KF-TARCH
Log L -411.0060 -400.5679 -400.5625 -396.6206 -418.1397
AIC 840.0120 821.1358 823.1250 813.2412 858.2794
BIC 862.2052 845.7949 850.2500 837.9003 885.4044
α1 0.2978 0.8491 0.8583 0.4955 0.3127
(0.1587)*** (0.2174)*** (0.3270) *** (0.1756)*** (0.1724)**
α2 1.4101 4.9388 4.9758 3.4791 2.5643
(1.6117) (1.1486)*** (2.1719) *** (1.3185)*** (0.2132)***
α3 0.0686 -0.1194 -0.1222 -0.0300 -0.0033
(0.0368)*** (0.0916) (0.0948) *** (0.0572) (0.0127)
α4 0.4276 -0.9411 -0.9832 -0.7277 -0.3142
(0.2147)*** (0.3196)*** (0.4533) *** (0.2706)*** (0.1420)***
S11 11.2593 6.6811 6.6321 9.5293 -10.8421
(0.9191)*** (0.9481)*** (2.9245) *** (1.6049)*** (1.2891)***
S12 -0.9673 -0.4622 -0.0771 0.2042 0.6001
(0.3449)*** (1.7635) (1.1177) (3.6211) (1.1023)
S22 0.0011 1.3537 1.3368 1.3921 -1.9273
(0.7422) (0.3626)*** (0.0708) *** (0.2984)*** (0.5037)***
δ0 / λ0 5.5325 0.2251 0.2271 0.0766 0.8355
(1.3367)*** (0.0658)*** (0.0124) *** (0.1159) (0.2885)***
δ1 / λ1 0.8485 0.3402 0.3385 0.9890 1.0614
(0.1614)*** (0.0473)*** (0.0000) *** (0.4312)*** (0.2753)***
δ2 / λ2 0.6596 0.6613 0.4021
(0.0469)*** (0.0000)*** (0.0827)***
δ3 / λ3 0.6264 0.3043
Note: *** and ** denote significance at 1% and 10% level respectively
Table 3: Dynamic between KLCI and FKLI for Kalman filter-ARCH-type models
Parameter KF-ARCH KF-GARCH KF-GARCH-M KF-EGARCH KF-TARCH
Log L -220.7034 -208.0228 -207.5728 -222.3188 -209.6269
AIC 459.4068 436.0456 437.1456 464.6376 441.2538
BIC 481.6000 460.7047 464.2706 489.2967 468.3788
α1 -0.1080 -0.0651 -0.0656 -0.0113 -1.9520
(0.1061) (0.1499) (0.1498) (0.0201) (0.4376)***
α2 0.1707 -0.1031 -0.1079 0.0195 2.8975
(0.1708) (0.3030) (0.3244) (0.0199) (0.4813)***
α3 0.0065 0.0282 0.0266 0.2498 -1.3473
(0.1668) (0.1477) (0.1461) (0.0158)*** (0.4302)***
α4 -0.0352 0.0675 0.0725 0.0870 2.0218
(0.1273) (0.1813) (0.1853) (0.0162)*** (0.4476)***
S11 1.0729 0.00002 1.8238 0.0001 -0.000003
(0.4040)*** (0.0749) (0.6309)*** (0.0288) (0.0652)***
S12 1.5286 1.8663 1.3567 1.3756 0.1058
(0.4082)*** (0.6987)*** (0.0624)*** (0.0265)*** (0.4949)
S22 0.00001 1.3990 0.000007 0.9177 0.5602
(0.0253) (0.6914)*** (0.0057) (0.0202)*** (0.4940)
δ0 / λ0 79.4829 0.1475 0.0560 3.4175 7.6290
(20.3967)*** (0.2119) (0.0037)*** (0.2865)*** (3.5286)
δ1 / λ1 0.2023 0.1404 0.1434 0.1303 -0.0244
(0.1797) (0.0002)*** (0.0000)*** (0.0499)*** (0.0690)***
δ2 / λ2 - 0.8591 0.8564 - 0.7138
(-) (0.0002)*** (0.0000)*** (-) (0.1024)
δ3 / λ3 - - - -0.4882 0.4612
(-) (-) (-) (0.2457)*** (0.1990)***
γ - - 0.1282 - -
(-) (-) (0.1319) (-) (-)
Note: *** and ** denote significance at 1% and 10% level respectively.
For GARCH model, it is noted that the ARCH and GARCH terms (0.1404 and 0.8591
respectively) sum to be less than unity. Therefore, the sample estimation holds the stationarity
condition for both the ARCH and GARCH models. Besides, it is found from KF-GARCH-M
model that the coefficient on the expected risk, γ is not statistically significant (0.1282). Thus,
the result provides no evidence of risk-return trade-off in the Malaysian stock market. In addition,
both the KF-EGARCH and KF-TARCH models suggest the existence of leverage effect in the
Malaysian stock market.
This study makes use of Kalman filter and variety of ARCH-type models to investigate
the feedback causal relationship between stock prices with each of currency exchange and
derivative product. There are five ARCH-type models used namely ARCH, GARCH, GARCH-
M, EGARCH and TARCH models. It has been frequently demonstrated that the GARCH(1,1)
process is able to present the majority of financial time series and there is a tendency to favour the
GARCH(1,1) model above other higher order of GARCH models. Therefore, this paper considers
only the GARCH(1,1) process. In general, the results show that dynamic linkages between KLCI
and FKLI are relatively weak. For the asymmetry TARCH models, there is a bi-directional
causality runs between KLCI and FKLI. On the other hand, the symmetry ARCH, GARCH and
GARCH-M models fail to reveal any recognizable pattern between the two variables. On the
other hands, many of the relationships between the KLCI and STL series are significant. The
results suggest that only KF-GARCH-M model has a bi-directional feedback effect between
KLCI and STL. In addition, the result proves the existence of leverage effect in the stock market.
However, the there is no evidence of risk-return trade-off in the Malaysian stock market.
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