Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Time – Varying World Integration of the Indian Stock Market:
A KALMAN Filter Approach
Srinivasa Rao Gangadharan1, C.A.Yoonus2 and Dilipkumar3
This paper examines the impact of World Financial Crises on the
time varying World integration of the Indian Stock market. Using
the weekly World Index, Nifty Dollar Index and the risk-free US T
– Bill from January 2, 2000 to 4th September 2011 we have
computed a theoretically more appropriate return index that
captures the sensitivity of an index to market risk with the help of
the Capital Asset Pricing Model (CAPM). We have employed
Kalman filter technique to examine the time varying market
integration of the Indian Stock market with the World Market.
Our findings reveal the Indian and the World markets are co
integrated and the recent World financial crisis did not cause any
impact on the integration structure between the Indian and the
World market.
Key words: KALMAN Filter, International Capital Asset Pricing Model (ICAPM), World
Index, Nifty Dollar Index, US Treasury Bill, time – varying co-efficient.
Introduction
Looking back at the decade of 2000, nearly half of this period the World Economy has
been under crisis. It all began with the bursting of the dotcom bubble (March 11, 2000 to
October 9, 2002), followed by commodity prices rise across oil, minerals and food (late
2004 to late 2007) and the ongoing World Financial Crisis (2007-12). The dotcom crisis,
wiped off $5 tn of poor investors wealth, dwindled the number of internet and technology
related IPOs (from 457 in 1999 to 76 in 2001) and destroyed 78 per cent (from 5047 fell
to 1114) of the value of Nasdaq Composite.
The World Financial Crisis (GFC) crippled the liquidity of the stock market in many
countries. This has upset the plans of the corporate sector as it is the stock market that
provides resources in various forms for their projects involving heavy outlays. Besides
this, the fears associated with European debt crisis and the contagion effects have
turned the returns from the equity market negative in
2011-121. This has further
aggravated the problem of sourcing finance from the Stock Market. Adding oil to the
burning issue is the sustainability of the crisis with severity exemplified by the growing
unemployment rate higher than the one prevailed in 2008 and the expanding level of
public debt in all major advanced economies.
India is not an exception to this. The Indian Stock market has been sailing comfortably
in the stock market arena since 2000 due to its robust growth, a maturing economy with
relaxed regulations and heightened cross-border flow of capital. The news about the
1
Faculty, Institute for Financial Management and Research, Chennai, India
Research Scholar, Institute for Financial Management and Research, Chennai, India
3
Research Scholar, Institute for Financial Management and Research, Chennai, India
2
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
bankruptcy of Lehman Brothers Holdings and Merrill Lynch & Co. and these two have
invested in Indian firms as well prompted the Foreign Institutional Investors (FIIs) huge
withdrawal of investment2 from the Indian Equity Market partly as a flight to safety and
partly to meet their redemption obligations at home. These withdrawals drastically pull
down the stock prices to more than 70 per cent from their peaks in January 2008 and
some have even lost to around 90 per cent of their value. The fears of recession in US
and high volatility in Sensex index caused Indian investors lose $131 billion 3 within
seven trading sessions.
Besides this, the revised guidelines of the Securities Contract Act, stipulated a minimum
public shareholding of 25 percent by all listed companies. This ushered companies both
private and public sector to a debate on whether to remain listed on stock exchanges or
opt for delisting.
We are primarily motivated by the following factors to undertake this study:First, a research paper (Bit-Kun Yeoh, Chee-Wooi Hooy and Zainudin Arsad, 2010) that
examined the Time-Varying World Integration of the Malaysian Stock Market using the
Kalman filter approach prompted us to undertake a similar study with respect to the
Indian Stock market.
Second, a study on how India has integrated with the World market in the last 12 years
(2000 to 2011) when the World Economy for nearly half of the period has been under
crisis would be interesting and facilitate the Indian policy makers in devising ways to
turn the economy from the crisis to the growth path.
Third, the data and the technique used in this study is something unique. Many studies
on stock market integration are static that does not consider time-varying nature of the
returns from the stock market. This study uses a theoretically more appropriate data
that captures the sensitivity of an index to non-diversifiable risk and a dynamic timevarying mathematical model known as Kalman filter technique.
Fourth, a study on stock market integration is prominent for investors, as they influence
international asset allocation potential and portfolio diversification decisions that
enhance the economic growth of a country. An important benefit of the internationally
integrated stock markets is International risk sharing. They induce a portfolio to shift
from a safe, low – return investments to high return investments that accelerates
productivity growth that ultimately stimulate economic growth (Ross Levine & Sara
Zervos, 1998).
So this paper by using the data computed from the CAPM and employing Kalman Filter
examines the impact of the financial crisis of the 2000s on the level of integration of the
Indian Stock market with the World.
The paper has been organized into four sections:
Section – I – deals with Review of Literature - A brief review on the theoretical and
historical background of Financial Integration, issues related to stock market integration
in India and Worldwide and the time-varying dynamic integration of the World Market;
Section - II details data and methodology employed; Section - III explains the empirical
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
findings of the hypothesis developed and Section – IV Summaries the paper with a
conclusion.
Section – I
Review of Literature
Much of the economic literature on financial integration is dedicated on the International
Financial Integration, though domestic financial integration constitute a critical pillar of a
market based economy as they mobilize savings, allocate risk, absorb external financial
shocks and foster good governance. This is due to the theoretical literatures bestow to
the International Financial Integration. Many theoretical models have identified that
major benefits of international financial integration such as risk sharing and alleviation of
capital scarcity help enhance economic growth (Prasad et. al., 2003). Coming to the
cost side, the high volatility of capital flows and their misallocation exacerbate domestic
distortions that may hamper economic growth
Historical Background
Although the study of financial integration dates back to late 70’s, the number of studies
at that time was scanty due to conservativeness of the stock markets. However, the
financial markets, especially the stock markets, for developing and developed markets
have now become more closely interlinked despite the uniqueness of the specific
market and country profile. The earliest work that has been widely cited on the
relationship among national stock markets and on clarifying the benefits from
international portfolio diversification was that of Grubel (1968).
Studies on Financial Integration that covered large number of countries and for longer
periods reveal high level of increasing tendency of equity market integration and support
the notion of international diversification - Ripley,1973, Lessard, 1976, Wheatly, 1988,
Fischer & Palasvirta, 1990, Sheng & TU, 2000, Mukerjee and Mishra)
In the context of India, there are very few studies on financial integration between the
Indian and the International Stock Market. The outcomes of these studies are
dichotomized in results, where many found no evidence of systematic cyclical
component or periodicity of integration between India and other stock markets (Rao &
Naik, 1990, Kumar, 2002, Ignatius, 1992, Mishra, 2002, Sharma and Kennedy, 1977).
However, there are also studies that showed integration of Indian stock market with the
mature markets of the World (Hansda and Ray, 2002, Nath and Verma, 2003, Wong,
Agarwal and Du, 2005).
Financial Integration and External Shocks
Studies that examined financial integration in the background of external shocks reveals
that stock prices provide signals before a number of recessions (Fisher and Merton,
1984). Studies that examined the effect of 1987 crash concluded that the degree of
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
international co-movement in stock price indices has increased significantly since the
1987 crash. Equity volatility is more likely to become high during recessions and the US
stock market is more volatile than others (Hamilton and Susmel, 1994, Lee and Kim,
1994, Jeon and Von-Frustenberg, 1990). Studies by Cheung (1997) and Yang et al.
(2003) applying Vector Auto Regressive (VAR) to examine market integration showed
that stock market integration changes over time especially during period marked by
financial crisis.
Literature on time-varying dynamic integration
Earlier studies on market integration use non-asset pricing models such as tracking the
correlation coefficients across national equity returns over time, Factor analysis to
explore interrelationships between the stock prices series (Ripley, 1973), Cluster
analysis (Panton et al, 1976), Spectral method (Hillard,1979), inter-temporal patterns of
the correlation coefficients among international stock markets (Maldonado and Saunder,
1981) that concluded pair-wise correlation coefficients are generally low and unstable.
These studies that tested correlation, lead-lag and volatility transmission are Static in
nature.
The concept of co integration gained momentum by Engle and Granger (1987) in their
attempt to study long-term relationship between financial markets. Literature reveals
that regulators and researchers preferred co integration analysis as it is a standard,
quantifiable, price-based financial integration method that exhibit common stochastic
trends that dominate the behavior of the co integrated markets in the long run. It limits
the number of independent variation and diversification opportunities between these
markets. Unfortunately, Co-integration analysis fails to take into account that
convergence is a gradual and on-going process. It only tests for convergence over the
whole period under consideration rather than investigating the degree of convergence
that increased more recently than earlier in time.
Many studies that employed co integration analysis to examine the level of integration
among different equity markets finds a single common trend implying that the returns in
all these markets are highly integrated - Kasa,1992, Cheung and Liu,1994, Corhay et
al.,1993, Engsted and Lund, 1997, Chen et al.,2002, Yang et al. 2003), and Fraser and
Oyefeso 2005.
These studies treat convergence as a static concept rather than as a gradual and an
on-going process. Serletis and King (1997), Rangvid (2001), Pascual (2003) and
Gilmore et al. (2008) utilize the same framework of co-integration analysis but focus on
the dynamic process of convergence using either the Kalman filter, or recursive and
rolling cointegration analysis to study the stock market integration. Fraser, Helliar and
Power,1994, Serletis and King,1997) and Manning, 2002 focused on Dynamic
Integration using the methodology proposed by Haldane and Hall (1991) for measuring
the convergence of the European equity markets.
Rangvid (2001) takes the effort to detect time-varying co-integration using a recursive
method. Pascul (2003) argued that increasing convergence shown by Rangvid may be
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
due to an increasing sample size over time. He conducted a rolling co integration test
with a fixed sample size and showed no evidence of increasing co integration among
markets.
Section – II
Data and Methodology
Data
The most widely used data to examine the level of stock market integration between
countries is the returns from their market index. A theoretically more appropriate data
that captures the sensitivity of an index to non-diversifiable risk (also known as Market
risk) is better suited for examining the level of integration rather than the index returns.
A market is completely integrated with the world if its assets have the same expected
return as the assets with identical risk levels listed in major World markets (Bekaert and
Harvey, 1995). The Capital Asset Pricing Model (CAPM), a standard model in Finance
postulates a stable linear relationship between the expected excess return and the nondiversifiable risk of holding a financial asset. So the Return data for examining the level
of Stock Market Integration between India and the World has been computed through
the Capital Asset Pricing Model (CAPM). To suit the international settings, the domestic
CAPM has been extended to a single factor International CAPM (ICAPM) that can be
written as
Ri,t  RF ,t  i  i ( Rw,t  RF ,t )   i,t
t = 1,2,3,……..N --------------- (1)
Where Rit, Rw,t and RF,t refer to the returns for the Market portfolio, World Portfolio and
International Risk free rate respectively; t represents the time period with sample size N;
i refers to the stock markets being studied and εi,t is the residual.
We have used the weekly World Index (Rw) and its corresponding weekly Nifty dollar
Index (Ri) to represent the World and Market portfolio. The rationale for using the
weekly rather than daily data is to arrest the noise arising out of the daily data. For the
“risk – free” rate we have used the short-term 90-day (3 month) US Treasury T-Bill as it
is the most risk-free rate available (i.e., it does not include maturity, liquidity, or default
risk).
All the three data - World Index, Nifty dollar index, 3 month US T-Bill has been sourced
from the Reuter database. The data series are in common currency that is US dollar to
alleviate any exchange rate noise. So the Risk – Return relationship is unaffected by the
choice of the reference currency. The data covered a time-period 2nd January, 2000 to
4th September, 2011. The returns from the indices are computed using the continuous
compound method as follows:
 CPt 

Rt  log
CP
 t 1 
……………………… (2)
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
CPt is the closing index in period t and CPt-1 is the closing index of the previous day.
Methodology
The traditional CAPM uses only one variable, beta, to describe the returns of a portfolio
or stock with the returns of the Market as a whole. In contrast the intercept (α) term in
the CAPM is used as a measure to evaluate the ability of the investors in selecting the
stocks and his skill in investing in the market at the appropriate time (Prather, Bertin and
Henkar,2004, Abdullah & Abdullah, 2009). It is also used to examine the level of stock
market integration. According to Korajczyk (1996) and Levine and Zervos (1998), if a
stock market is perfectly integrated with the world, then the intercept (α i) that represents
the pricing error should be equal to zero. The CAPM’s prediction for the intercept is that
it should equal zero and the slope (β) should equal the excess returns on the market
portfolio.
Levine and Zervos (1998) proposed that the estimates of stock market integration can
be represented by the absolute value of αi and multiplying it with negative one. In other
words, the adjusted market integration index can be expressed as
MII =
-|άi,t|
This index is designed to be positively correlated with the degree of market integration.
The index can take any value with the upper brand equal to zero, and a zero index is
interpreted as stock market i that is perfectly integrated with the World Market.
The Ordinary Least Square estimation of Equation (1) is straightforward; in practice,
however, it is unreasonable to allow the level of integration to be constant as the risk is
usually found to vary over time. The estimation of ICAPM coefficients using the OLS
regression may be less desirable from economic and financial points of view, which
limits researchers in matching the levels of market integration with the economic or
financial events that have taken place over the same period. In this study, we employed
a time-varying coefficient technique to capture the time varying market integration
process.
Estimating Time –Varying Integration with the Kalman Filter
Technique
The Kalman Filter Technique allows for the estimation of both (a) a time – varying
intercept (α) and time-varying co-efficient (β) of ICAPM. It is a repeat procedure that
progresses through the data and yields at each time “t” a minimum mean-square linear
estimate of the state variables and a covariance (Risk of Stock1 x Correlation of Stock1
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
& Stock2xRisk of Stock2) matrix of the estimate. Kalman filter approach makes use of a
state space model of (N x 1) vector Yt as a function of Xt.
Yt   t  t X t   t ……………………………………
(3)
t = 1,2, 3,…….n. Where α = Intercept, β = coefficient, ε = error term
Equation (1) is observation equation.
 t   t 1  nt
……………………….(4)
State equations
 t   t 1  vt …………………… ..(5)
αt and βt are allowed to vary over time according to a random walk process. The random
walk model is quite general in nature because it covers a large number of time paths or
gradual coefficient variation reasonably well. It also allows a gradual level shift in the
parameters.
So equation 1 can be rewritten as
Yt   t zt   t .
…………………………..(6)
zt  AZ t 1  wt ……………(7)
Where Zt is the vector of time varying parameter (αt,βt). It allows a gradual level shift in
the parameters. δ is the vector of the constant and A is the identity matrix. εt and wt are
error terms that are assumed to be independently distributed as
εt~IID(0,ζ2) and wt~IID(0,Q) --------------------------- (8)
In this model there are three unknown parameters (hyper parameters) that must be
estimated (1) Diagnol elements of Q and the (2) Variance of the observation equation
and (3) ζ2
The Kalman filter equations are obtained by defining Z t = Vector of the State Variables
at time “t” and Pt as the covariance matrix of the state vector. Besides that Zt (t-1) is the
best estimate of Zt based on information up to t-1, while Pt(t-1) is the covariance matrix of
Zt(t-1). The prediction equations are expressed as
Z t (t 1)  Az (t 1)
………………9
Pt (t 1)  APt 1 A1  Q.
………………10
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Equation – 9, the one-step-ahead prediction of the state is formed by taking the last
known value of the variables and multiplying it by the transition matrix A. Similarly, the
estimate of the covariance matrix of the state prediction in Equation (10) also utilizes
past data. So we have two estimates. We need to calculate (a) one-step-ahead
prediction error et (b) and its covariance ft
et  Yt  Z t (t 1) .............(11)
f t  Pt (t 1) /    .........(12)
The et contains new information about Zt beyond that contained in Zt|t-1. Therefore,
after observing Yt ,the one-step-ahead of the state may be improved by incorporating
this new information. The updated equations for the estimates of the state and its
covariance matrix are expressed as
Zt = Zt|t-1 + Pt|t-1 δ’ ft-1et ------------------------------ (13)
Pt = Pt|t-1 - Pt|t-1 δ’ ft-1 δ Pt|t-1 ------------------------ (14)
Then the process returns to equation (9) for the next iteration
From the discussion above, it can be seen that the hyperparameters of Equation (8)
are unknown and thus need to be estimated. Under the assumption that ε t and wt are
normally distributed, the sample log likelihood can be expressed as below to estimate
the unknown parameters of the system equations:
Log L = -
log 2π∑
|- ∑
---------------- (15)
The likelihood is evaluated using Kalman Filter estimates and must be maximized with
respect to the unknown parameters.
By employing the Kalman Filter methodology mentioned above, the time-variant ICAPM of equation (1) can be expressed as a time-varying ICAPM as follows:
Ri,t – RF,t = αi,t + βi,t (Rw,t – RF,t ) +εi,t
----------------------------------------- (16)
Hence, the statis MII of equation (2) attempts to be expressed via time-series behavior
as
MII =
-|άi,t|
We have used MATLAB sotware to compute the Time – Varying intercept coefficient
through Kalman Filter Model.
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Section – III
Empirical Analysis
We begin our analysis with some important descriptive summary statistics of the weekly
returns of the World and Indian Stock market indices (Table – I). The Mean weekly
return for India is positive with 0.1 per cent and for the World it is negative with -0.01 per
cent. The Standard deviation of the weekly return for India (1.72) and World (1.09)
shows that Indian Stock market is more risky than the World Market.
The maximum return from the Indian market is positive 8.48 per cent nearly double that
of the World Stock market. The Minimum for both the World and India is negative.
Coming to the distribution we find both World and the Indian return data are skewed to
the left. Data that are skewed to the left have a long tail that extends to the left are
negatively skewed. The Kurtosis value indicates that both the series are leptokurtic.
Stationarity of the Variables
Before proceeding further, it is customary to check the stationarity of the time series to
test the presence of unit root. Because, empirical analysis of large time series data
assumes that the underlying time series is stationary. Besides this, regressing one time
series variable on another time series variable, one often obtains a very high R 2
although there is no meaningful relationship between the two.
This type of situation displays the problem of spurious regression. This problem arises
because if both the time series exhibit strong trends (sustained upward or downward
movements), the high R2 observed is due to the presence of the trend, and not due to a
true relationship between the two.
The Phillips – Perron (PP) and Augumented Dicky Fuller (ADF) tests were conducted
on the excess return of the Indian Portfolio (Ri,t - RF,t) and on the excess return of the
World Portfolio (Rw,t - RF,t) because the International Capital Asset Pricing (ICAPM) is
expressed in terms of excess returns.
The unit root tests were conducted with intercepts and two alternative trend
assumptions, - with and without trend. The results of ADF and PP test given in Table –
II shows that “P” value is zero in all cases which means the values are falling under
rejection area. This makes us to infer the presence of no unit root in the difference in all
the four cases and the series is stationary. The lags for the unit root test are determined
by the Schwartz Bayesian Information Criterian (SBIC).
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Computation of Market Integration
We need to have a bench mark estimate to compare the dynamic time-varying
coefficient and the static coefficients to determine the much preferred unbiased
statistical parameter that measures the level of integration between the two indices. So,
as a first step we computed the static coefficients through the Ordinary Least Square
(OLS) regression method as a bench mark to compare the time-varying coefficient
through Kalman Filter Model. The results of the static coefficient estimated through the
OLS equation (1) is displayed in Table - III
Ri ,t  RF ,t  i  i ( Rw,t  RF ,t )   i ,t
t = 1,2,3,…n------------ (1)
Ho - Null Hypothesis - Intercept (α) = 0. Reject Ho if “t” value > 1.96 @ 5% level of
significance
H1 - Alternative Hypothesis - Intercept (α) ≠ 0
The alpha coefficient indicates how an investment has performed after accounting for
the risk it involved. In an efficient market, the expected value of the alpha coefficient is
zero. Our results indicate that alpha coefficient is insignificant at 5% level of significance
and hence we say that ICAPM is a well specified the data set.
With α = 0.099 we proceed to compute the Time – Varying coefficient through the
Kalman filter model. We have developed the following hypothesis
H0 (Null Hypothesis) = MII is insignificant which means there is integration of Indian
Market with the World Market.
H1 (Alternative) = MII is significant which means there is no integration of the Indian
Market with the World Market.
We have used the Kalman Filter Model and computed time varying intercepts coefficient (Alpha) from 02nd January, 2000 to 24th July 2011. Through this we have
computed 604 time-varying alphas. For these alphas we need to compute the upper
and lower confidence intervals and built the band through the following equation.
MII ± 1.96 * Standard Error
The intercept computed through OLS is 0.09907 and the standard error is 0.059618, the
“t” value for 95% level of test significance is 1.96. So Upper Limit Upper Level
Confidence Interval (ULC) = 0.09907+0.059618*1.96 = 0.215921
Lowe level Confidence Interval (LLC) = 0.09907-0.059618*1.96= - 0.01778
MII is plotted in Figure – 1.
We need to see whether our average MII falls within the band or violate the band limit.
The average alpha value of the OLS estimate (0.0991) and the average alpha
computed through Kalman Filter (0.0847) are more or less very close and fall within the
band. This gives us the signal of co integration between the Indian and World market.
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Another supporting evidence for the existence of co integration between India and the
World Market is that the “t” value 1.42 is less than the critical value of 1.96. @ 95
percent confidence level that do not reject the null hypothesis which had no wide
variation between India and the World stock market. We have also tested the integration
between India and the World with Joansan Cointegration analysis and that also gives
the same result. So we conclude that in the last 12 years from January 2000 to
November 2011 the World financial crises have not brought any impact on the level of
integration between India and the World.
End Notes
1. Most of the equity markets (Spain and Italy) in the world returned negative returns to
investors. US, Japan and Mexico were out of this due to a number of stimulus measures
such as economic growth, improving employment conditions, enhanced credit take off,
revival of domestic industry and rehabilitation of the tsunami affected stakeholders etc.
taken by the government.
2. The FIIs had invested over Rs 10,00,000 crore between January 2006 and January
2008, driving the Sensex to its historical high level of 21,000 points on January 8, 2008 .
But from January, 2008 to January, 2009, FIIs pulled out from the equity market as the
withdrawals drove the Sensex down to less than 9,000 in a year, the level it had three
years back. Similar trend has also been observed for the S & P CNX Nifty.
3. On May 22, 2006, the SENSEX plunged by 1100 points during intra-day trading,
leading to the suspension of trading for the first time since May 17, 2004. The volatility
of the SENSEX had caused investors to lose Rs 6 lakh crore (US$131 billion) within
seven trading sessions.
Table - I
Descriptive Statistics - Summary
Statistics of weekly returns
Statistical Parameters
Max
Min
Mean
Standard deviation
Skewness
Kurtosis
India
World
8.48
4.66
-8.48
-9.26
0.10
-0.01
1.72
1.09
-0.57613 -1.16123
6.13
13.06
Proceedings of 3rd Asia-Pacific Business Research Conference
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Table - II
Augumented Dicky Fuller (ADF) and Phillips – Perron (PP) Unit Root tests of
excess returns of the Indian and World portfolios
Series
Lag
Ri,t - RF,t
1
Rw,t - RF,t
0
Ri,t - RF,t
4
Rw,t - RF,t
4
***
Without
Intercept and
Trend
ADF test
-15.053***
[0.000]
-25.197***
[0.000]
PP test
-22.924***
[0.000]
-25.191***
[0.000]
With
Intercept
With
Intercept
and Trend
-15.051***
[0.000]
-25.255***
[0.000]
-15.084***
[0.000]
-25.308***
[0.000]
-22.921***
[0.000]
-25.247***
[0.000]
-22.933***
[0.000]
-25.297***
[0.000]
means significant at 1% level of significance.
Table - III
Results of the Ordinary Least Square Estimation
Variable
co-efficient
t-statistic
Standard
Error
α - Intercept
β
R w ,t  R F , t
0.099
1.6617
0.0596
0.834
15.2151*
0.0548
* denotes significance at 5% level
Proceedings of 3rd Asia-Pacific Business Research Conference
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Table - IV
Results of the Kalman Filter Technique
Parameters Alpha Beta MII LCI UCI SE
Average 0.0847 0.82959 -0.0847 -0.2159 0.17781 0.05962
Computed " t" Value = (MII/SE) 1.4207
Critical Value (CV) = 1.96 @ 95% level of significance
MII
Market Integration Index
LCI
Lower Confidence Interval
UCI
Upper Confidence Interval
Figure – 1
Time – Varying Market Integration Index
MII
1
33
65
97
129
161
193
225
257
289
321
353
385
417
449
481
513
545
577
-0.08458
-0.08474
-0.08491
MII
Proceedings of 3rd Asia-Pacific Business Research Conference
25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1
Figure -2
MII with the band (Lower and Upper Confidence Intervals)
0.2
0.15
0.1
0.05
MII
-0.05
1
32
63
94
125
156
187
218
249
280
311
342
373
404
435
466
497
528
559
590
0
LCI
UCI
-0.1
-0.15
-0.2
-0.25
Outer band represents the confidence intervals.
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