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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 25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1 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 25 - 26 February 2013, Kuala Lumpur, Malaysia, ISBN: 978-1-922069-19-1 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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