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\title{The Lead-Lag Effect on the Predictability of Returns: The Case of Taiwan Market}
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             \author[1]{Latifa Fatnassi  Chaibi}

             \affil[1]{  Faculty of Economics and Management, Tunis, Tunisia}

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\date{\small \em Received: 7 December 2013 Accepted: 4 January 2014 Published: 15 January 2014}

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\begin{abstract}
        


The aim of this paper is to investigate the lead-lag effect on the predictability of returns. This analysis is applied to daily and one-minute interval data on the TAIWAN stock market. The results indicate evidence of predictability between indices with different degrees of liquidity and when considering one-minute interval data. 

\end{abstract}


\keywords{small enterprises, funding institutions, microfinance.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
he lead lag effect according to Tonin et al. (  {\ref 2013}) is perceived when there is a relationship between the price movements of two distinct markets, when one of them leads and the other follows with some lag time when this effect is identified, there is a rupture of the Efficient Market Hypothesis (EMH) in consequent the predictability of returns.\par
Several studies have investigated the lead-lag effect on the predictability i.e. Lo and  {\ref Mackinlay (1990)},  {\ref Camillerie and Green (2004)}. All the studies conclude that the predictability is attributed to the lead-lag effect. Thus, study aims to examine the lead-lag effect and its impact on predictability of returns of Taiwan stock market. To this end, this paper is organized as follow: in the first section, we go through a literature review of the lead-lag effect. In the second section, we presented the data and methodologies. The empirical results are summarized in the third section. 
\section[{II.}]{II.} 
\section[{Literature Review}]{Literature Review}\par
Camilleri and Green (2004) examined the leadlag effect on the Indian market using three approaches: Test Pesaran Timmermann, VAR model, Granger-Causality and Impulse-response function on daily and high frequency data. The results imply that lead-lag effect appears to be the main source of the predictability of returns. \hyperref[b0]{Oliveira et al. (2009)} examined the existence of lead-lag effects between U.S stock market (NYSE) and the Brazilian stock market (Bovespa). They concluded that the price movement in the NYSE is followed by similar movements in Bovespa which would enable predicting stock prices in the Brazilian market, thus providing arbitrage opportunities.\par
The aim study of Tonin et al. (  {\ref 2013}) is to examine the lead lag effect between the stock market of the BRIC member countries from March 2009 until to March 2013. The result emphasizes that the Brazilian market leading others stock exchange analyzed in periods before and after the financial crises. TSE (1995) examined the lead-lag relationship between the Nikkei spot and futures contract about Nikkei index and found that lagged changes in futures prices cause adjustments in the spot price, in the short run, but the reserve is not true. \hyperref[b2]{Meric et al. (2008)}, study the co movement and causality to markets in the United States, United Kingdom and six asian markets. The authors used the technique of Principal Analysis to determine if the standards of co movement of the markets of USA, UK, AUSTRALIA, CHINA, RUSSIA, INDIA, JAPAN and SOUTH KOREA have changed with periods before and after September 11 th , 2001.\par
Pena, Guelman and Rabelo (2010) analysed the relationship of Dow Jones index and the Nikkei-225 index with the Bovespa index with daily data of the variation of three indexes in the period of January 2006 to May 2008. The results identified contemporary relations between Dow Jones and Bovespa indexes. The authors also indicate the possibility of lag in the relationship between Bovespa and Nikkei 225 indexes. \hyperref[b4]{Nakamura (2009)} shows the existence of leadlag effect between the equity markets and the integration of the Brazilian stock market and their deposits in the American depositary receipt (ADR s).\par
Mulliaris and Urratia  {\ref (1992)} shows that the leadlag effect for six major stock market indexes, comaparing these indices between the periods before and after the crises of 1987 submitted significant changes between those periods. 
\section[{III.}]{III.} 
\section[{Dat nd Methodology}]{Dat nd Methodology}\par
The analysis of the lead-lag effect on the predictability of returns is applied on the daily and high frequency data of Taiwan stock exchange. The daily set constitutes of the closing observations of the TSEC (Taiwan stock exchange corporate) and the TSEC Midcap. The main and the less liquid index respectively. The daily data period ranges from 30/04/2002 to 05/04/2012.the high frequency data included the value of both indices and the study period lasts between 03/03/2012 to 07/03/2012. We begin first by the unit root test (ADF). Subsequently, we will analyze the lead-lag effect on the predictability of return using three The Granger-causality methodology is based on the estimated VAR. Granger  {\ref [1969]} showed that a shock affects a given time series, generates a shock to other time series and then the first series is due to Granger in the second. In this case, the VAR model of a time series appears to be an AR adjusted under other delayed time series and an error term. The VAR model is a means of modeling causal and feedback effects (feedback effect) when two or more time series according to Granger cause the other. The term does not imply causality; it may be the case of inter-relationships between time series caused by an exogenous variable. A bivariate VAR model may be formulated as follows:t n i i t i n i i t i t y x x 1 1 1 1 1 (1) t n i i t i n i i t i t y x y 2 1 2 1 2 (2)\par
Where t x and t y are two variables assuming to Granger-cause each other, whilst t is an error term.\par
The system of two equations (  {\ref 1}) and (  {\ref 2}) is formulated by the following vector: The Granger causality implies market inefficiency in the sense that fluctuations generate an index fluctuation leads to a fluctuation in another index. This means that if the first fluctuation was justified by new information, the latter fluctuation should have occurred at the same time, ruling out lead-lag effects. Therefore when testing for Granger-Causality using daily data, one should expect contemporaneous relationships if the markets are efficient and if there are not nonsynchronous trading effects. 
\section[{Impulse-Response Function}]{Impulse-Response Function}\par
One of the main uses of the VAR process is the analysis of impulse response. The latter represents the effect of a shock on the current and future values of endogenous variables. VAR models can generate the Impulse-Response Functions. The response of each variable in the VAR system to a shock affecting a given variable: either a shock on a variable t x , can directly affect the following achievements of the same variable, but it is also transmitted to all other variables through dynamic structure of the VAR. The impulse response function (IRF) of the variable t y to a shock on the variable t x , occurring in time t, can be viewed as the difference between the two time series:\par
The realisations of the time series t y after the shock in t\par
x has occurred; and\par
The realisations of the series t y during the same period but in absence of the shock in t\par
x .\par
This can be formulated in mathematical notation as follows: , is a shock at time t;1 t\par
is the historical time series is an innovation IRF is generated from t to t + n. 
\section[{IV.}]{IV.} 
\section[{Empirical Results}]{Empirical Results}\par
This section reports the results of the analysis of a lead-lag effect on the predictability of returns of Taiwan stock market. In both cases daily data and high frequency, the ADF test results show that the two indices are no stationary in level (ADF values are higher than their critical values for different significance levels). However, in first differences, the logarithmic price indices are stationary I (1). To clarify this idea of stationarity of the series, we turn to study the autocorrelation of TSEC (LT) and TSEC Midcap (LTM) series at different delays. The autocorrelation coefficients are high and decline slowly indicating the existence of a unit root. What is the evidence that the logarithmic series of two indices are I \hyperref[b0]{(1)}. In what follows, we analyze the lead-lag effect on the predictability of returns using three methodologies, namely the VAR, Granger causality and impulse response function.\par
According to both AIC and SC criteria we obtain a VAR (1) for the logarithmic daily and high frequency series of indices LT and LTM. Estimation of ndividual equations of the VAR systems are reproduced in table 1 (in APPENDIX)\par
The lead-lag effect between the two indices can be derived from a significance of the coefficients of two equations. From Table1, we can see that there is no lead-lag effect, since the coefficients of LKM (-1) and LK\par
The Lead-Lag Effect on the Predictability of Returns: The Case of Taiwan Market 2 Year ( ) a) (-1) are not significant at the 5\% and therefore it no relationship between the two indices. But in the the case of the high frequency data, we find that the coefficient that are significant indicating a led-lag effect and delayed returns of LTM can explain returns of the dependant variable LT.\par
In order to investigate further the Granger causality tests are applied to the system of two equations. The results obtained for a number of delay equal to one for daily and high frequency data are given in Table \hyperref[tab_1]{2}. The null hypothesis hypothesis that LTM does not cause LT is accepted when the probability associated is greater than the usual statistical threshold of 5\%. Similarly, the null hypothesis that LT does not cause LTM is accepted threshold of5\%. These different VAR performed in this section confirm the evidence of a relationship and the TSEC index generate TSEC Midcap in case of high frequency data.\par
The analysis of the Impulse-Response function of each indices and for both daily and high frequency data, reveals the following results: DAILY DATA HIGH FREQUENCY DATA If data is daily, a TSEC shock had a higher impact on the TSEC Midcap index. For the case of oneminute frequency, a TSEC shock generates a higher impact on the TSEC Midcap index. This is attributed to a lead-lag relationship.\par
This study, based on impulse response functions, can be supplemented by an analysis of variance decomposition of forecast error. The objective is to calculate the contribution of each of the innovations in the variance of the error. The results for the study of the variance decomposition are reported in a Table \hyperref[tab_2]{3}. The variance of the forecast error is due to LT for about 99.97\% to its own innovations and to 0.02\% with those of LTM. The variance of the forecast error is due to LTM 0.067\% to the innovations of LT and 99.93\% to its own innovations. We can deduce that the impact of a LT shock on LTM is important but there is almost lower than the impact of a LTM shock on LT. For the case of high frequency data: The variance of the forecast error of LT is due to 8\% of LTM innovations while that of LKM 75.09\% is due to innovations LT. So the impact of a LT shock on LTM is more important than the impact of a LTM shock on LT: These results concluded that the predictability of LTM index by LT returns. These results are consistent with those shown by the impulse response function. In these studies, we can conclude that the lead-lag effect can generate a predictability of returns of the two indices of Taiwan stock exchange in the case of frequency data.\par
V. 
\section[{Conclusion}]{Conclusion}\par
The purpose of this chapter is to study the impact of the lead-lag on the predictability of returns Taiwan stock exchange via the examination of effect. Three methodologies were adopted on daily and high frequency data of two indices. These are different levels of liquidity based on bid-ask spread. Specifically, in the high-frequency data, the results show that the more liquid index leads the less liquid. In the conclusion the lead-lag effect cause the predictability returns on the Taiwan stock exchange.\par
The Lead-Lag Effect on the Predictability of Returns: The Case of Taiwan Market 2 Year ( )\begin{figure}[htbp]
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\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Degrees of\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep Exclude\tabcellsep Chi-sq\tabcellsep Freedom\tabcellsep Prob.\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep LTM\tabcellsep 1.076101\tabcellsep 1\tabcellsep 0.29971\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep All\tabcellsep 1.076101\tabcellsep 1\tabcellsep 0.29971\\
\tabcellsep \multicolumn{3}{l}{Granger-Causlity Test}\tabcellsep \multicolumn{2}{l}{Dependent variable: LTM}\tabcellsep \\
\multicolumn{2}{l}{Dail y data Null Hypothesis LTM does not Granger Cause LT}\tabcellsep F-Statistic 0.42530\tabcellsep Probability 0.51441\tabcellsep Exclude LT All\tabcellsep Chi-sq 0.493649 0.493649\tabcellsep Degrees of Freedom 1 1\tabcellsep Prob. 0.48248 0.48248\\
\multicolumn{2}{l}{LT does not Granger Cause}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
LTM\tabcellsep \tabcellsep 1.32350\tabcellsep 0.25015\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{VAR Pairwise Granger Causality}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{2}{l}{Dependent variable: LT}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep Degrees of\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Exclude\tabcellsep Chi-sq\tabcellsep Freedom\tabcellsep Prob.\tabcellsep \tabcellsep \tabcellsep \\
LTM\tabcellsep 0.425301\tabcellsep 1\tabcellsep 0.5143\tabcellsep \tabcellsep \tabcellsep \\
All\tabcellsep 0.425301\tabcellsep 1\tabcellsep 0.5143\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{2}{l}{Dependent variable: LTM}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Exclude\tabcellsep Chi-sq\tabcellsep Degrees of\tabcellsep Prob.\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \tabcellsep Freedom\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
LT\tabcellsep 1.323501\tabcellsep 1\tabcellsep 0.2500\tabcellsep \tabcellsep \tabcellsep \\
All\tabcellsep 1.323501\tabcellsep 1\tabcellsep 0.2500\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.14958985831469052\textwidth}P{0.5045488441461596\textwidth}P{0.005070842654735272\textwidth}P{0.02535421327367636\textwidth}P{0.16543624161073825\textwidth}}
\tabcellsep \tabcellsep \tabcellsep 1\tabcellsep 0.016367 24.50274 75.04973\\
\tabcellsep \tabcellsep \tabcellsep 2\tabcellsep 0.019423 24.90636 75.05936\\
\tabcellsep \tabcellsep \tabcellsep 3\tabcellsep 0.019435 24.91379 75.07862\\
\tabcellsep \tabcellsep \tabcellsep 4\tabcellsep 0.019435 24.91387 75.08861\\
\tabcellsep \tabcellsep \tabcellsep 5\tabcellsep 0.019435 24.91387 75.08861\\
\tabcellsep \tabcellsep \tabcellsep 6\tabcellsep 0.019435 24.91387 75.08861\\
\multicolumn{2}{l}{LKM series}\tabcellsep \tabcellsep 7\tabcellsep 0.019435 24.91387 75.08861\\
Données journalières\tabcellsep \tabcellsep \tabcellsep 8 9\tabcellsep 0.019435 24.91387 75.08861 0.019435 24.91387 75.08861\\
Variance\tabcellsep \tabcellsep \tabcellsep 10\tabcellsep 0.019435 24.91387 75.08861\\
Decomposition\tabcellsep \tabcellsep \tabcellsep Ordering: LT LTM\\
of LT:\tabcellsep \tabcellsep \tabcellsep \\
Period\tabcellsep S.E.\tabcellsep LT\tabcellsep LTM\\
1\tabcellsep \multicolumn{3}{l}{2.50E-09 100.0000 0.000000}\\
2\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97866 0.021340}\\
3\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
4\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
5\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
6\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
7\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
8\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
9\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
10\tabcellsep \multicolumn{3}{l}{2.50E-09 99.97865 0.021345}\\
Variance\tabcellsep \tabcellsep \tabcellsep \\
Decomposition\tabcellsep \tabcellsep \tabcellsep \\
of LTM:\tabcellsep \tabcellsep \tabcellsep \\
Period\tabcellsep S.E.\tabcellsep LT\tabcellsep LTM\\
1\tabcellsep \multicolumn{3}{l}{2.42E-09 0.065231 99.93477}\\
2\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067311 99.93269}\\
3\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
4\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
5\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
6\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
7\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
8\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
9\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
10\tabcellsep \multicolumn{3}{l}{2.42E-09 0.067312 99.93269}\\
Ordering: LT LTM\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{2}{l}{Intervalle d'une minute}\tabcellsep \tabcellsep \\
Variance\tabcellsep \tabcellsep \tabcellsep \\
Decomposition of\tabcellsep \tabcellsep \tabcellsep \\
LT:\tabcellsep \tabcellsep \tabcellsep \\
Period\tabcellsep S.E.\tabcellsep LT\tabcellsep LTM\\
1\tabcellsep \multicolumn{3}{l}{0.054759 100.0000 0.000000}\\
2\tabcellsep \multicolumn{3}{l}{0.067947 99.92130 0.078704}\\
3\tabcellsep \multicolumn{3}{l}{0.068060 99.91973 0.080267}\\
4\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
5\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
6\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
7\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
8\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
9\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
10\tabcellsep \multicolumn{3}{l}{0.068061 99.91972 0.080284}\\
Variance\tabcellsep \tabcellsep \tabcellsep \\
Decomposition of\tabcellsep \tabcellsep \tabcellsep \\
LTM:\tabcellsep \tabcellsep \tabcellsep \\
Period\tabcellsep S.E.\tabcellsep LT\tabcellsep LTM\end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 		 		\backmatter  			 
\subsection[{Appendix}]{Appendix}			 			  				\begin{bibitemlist}{1}
\bibitem[Meric et al. ()]{b2}\label{b2} 	 		‘co movements of US, uk and Asian stock markets before and after’.  		 			I Meric 		,  		 			S Kim 		,  		 			J Kim 		,  		 			H 		.  	 	 		\textit{Journal of Money}  		2008. September 11. 2001. p. 3.  	 	 (Investment and Brazilian) 
\bibitem[Tse ()]{b1}\label{b1} 	 		‘lead-lag relationship between spot price index and futures price of Nikkei stock average’.  		 			Y Tse 		,  		 			K( 		.  	 	 		\textit{Journal of Forecasting}  		1995. 14 p. .  	 
\bibitem[Malliaris and Urrutia ()]{b5}\label{b5} 	 		 			A G Malliaris 		,  		 			J Urrutia 		.  		\textit{the international crash of October 1987: causality tests. The Journal of Financial and Quantitative Analysis},  				1992. 27 p. .  	 
\bibitem[Nakamura ()]{b4}\label{b4} 	 		\textit{O efeito lead-lag entre o mercado acionário brasileiro e o mercado de ADRs: uma revisão metodológica},  		 			R M Nakamura 		.  		2009. 2009. Brasília. 58.  		 			Universidade de Brasília 		 	 	 (Monografia (Graduação em Administração)) 
\bibitem[Pena et al.]{b3}\label{b3} 	 		 			G E Pena 		,  		 			B Guelman 		,  		 			H Rabello 		.  		 \url{http://www.administradores.com.br/informe-se/producao-academica/influencia-dos-indices-dow-jones-e-nikkei-225-sobre-o-ibovespa/785/}  		\textit{Influência dos índices Dow Jones Industrial Avarage e Nikkei-225 sobre o Ibovespa. Faculdades Ibmec},  				 	 
\bibitem[Oliveira and Mederos ()]{b0}\label{b0} 	 		‘Testing the existence of lead-lag effects between the U.S and Brazilian stock market’.  		 			G Oliveira 		,  		 			O Mederos 		.  	 	 		\textit{Brazilian Businessreview, Vol6, Issue1},  				2009. p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
