ARTICLE
ABSTRACT
The mutual information coefficient is one of the most important generalizations of the Pearson correlation coefficient. Its advantage is that it is able to measure all kinds of dependencies, also nonlinear ones. Like the Pearson correlation coefficient, the mutual information coefficient may be applied to a single time series in order to identify serial dependencies. In this paper the log-returns of the selected Polish and foreign stock indices have been analyzed. By comparing the results obtained for the raw returns and the residuals of the fitted ARMA-GARCH models, the nature of the identified dependencies has been determined. Moreover, the bootstrap procedure has been applied to verify significance of the mutual information coefficients and, in consequence, to determine the number of lags in the analyzed series. In the most investigated indices, nonlinear dependencies different from the ARCH effect have been detected and lag = 1 was the dominant time delay in such situations.
KEYWORDS
mutual information coefficient, mutual information measure, lags, nonlinear dynamics, stock indices
REFERENCES
[1] Bruzda J., (2004), Miary zaleznosci nieliniowej w identyfikacji nieliniowych procesów ekonomicznych, Acta Universitatis Nicolai Copernici, 34, 183-203.
[2] Dionisio A., Menezes R., Mendes D.A., (2003), Mutual Information: a Dependence Measure for Nonlinear Time Series, working paper.
[3] Dionisio A., Menezes R., Mendes D., (2006), Entropy-Based Independence Test, Nonlinear Dynamics, 44, 351-357.
[4] Fiszeder P., Orzeszko W., (2012), Nonparametric Verification of GARCH-Class Models for Selected Polish Exchange Rates and Stock Indices, Finance a uver – Czech Journal of Economics and Finance, 62 (5), 430-449.
[5] Fonseca N., Crovella M., Salamatian K., (2008), Long Range Mutual Information, Proceedings of the First Workshop on Hot Topics in Measurement and Modeling of Computer Systems (Hotmetrics’08), Annapolis.
[6] Fraser A.M., Swinney H.L., (1986), Independent Coordinates for Strange Attractors from Mutual Information, Physical Review A, 33 (2), 1134-1140.
[7] Granger C.W.J., Lin J-L., (1994), Using the Mutual Information Coefficient to Identify Lags in Nonlinear Models, Journal of Time Series Analysis, 15, 371-384.
[8] Granger C.W.J., Terasvirta T., (1993), Modelling Nonlinear Economic Relationships, Oxford University Press, Oxford.
[9] Hassani H., Dionisio A., Ghodsi M., (2010), The Effect of Noise Reduction in Measuring the Linear and Nonlinear Dependency of Financial Markets, Nonlinear Analysis: Real World Applications, 11, 492-502.
[10] Hassani H., Soofi A.S., Zhigljavsky A.A., (2010), Predicting Daily Exchange Rate with Singular Spectrum Analysis, Nonlinear Analysis: Real World Applications, 11, 2023-2034.
[11] Maasoumi E., Racine J., (2002), Entropy and Predictability of Stock Market Returns, Journal of Econometrics, 107, 291-312.
[12] Orzeszko W., (2009), Współczynnik informacji wzajemnej jako miara zaleznosci nieliniowych w szeregach czasowych, Acta Universitatis Nicolai Copernici. Ekonomia, XXXIX, zeszyt 389 – Dynamiczne Modele Ekonometryczne, 157-166.
