Ozun, Alper and Cifter, Atilla (2007): Modeling Long-Term Memory Effect in Stock Prices: A Comparative Analysis with GPH Test and Daubechies Wavelets.
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Long-term memory effect in stock prices might be captured, if any, with alternative models. Though Geweke and Porter-Hudak (1983) test model the long memory with the OLS estimator, a new approach based on wavelets analysis provide WOLS estimator for the memory effect. This article examines the long-term memory of the Istanbul Stock Index with the Daubechies-20, Daubechies-12, the Daubechies-4 and the Haar wavelets and compares the results of the WOLS estimators with that of OLS estimator based on the Geweke and Porter-Hudak test. While the results of the GPH test imply that the stock returns are memoryless, fractional integration parameters based on the Daubechies wavelets display that there is an explicit long-memory effect in the stock returns. The research results have both methodological and practical crucial conclusions. On the theoretical side, the wavelet based OLS estimator is superior in modeling the behaviours of the stock returns in emerging markets where nonlinearities and high volatility exist due to their chaotic natures. For practical aims, on the other hand, the results show that the Istanbul Stock Exchange is not in the weak-form efficient because the prices have memories that are not reflected in the prices, yet.
|Item Type:||MPRA Paper|
|Original Title:||Modeling Long-Term Memory Effect in Stock Prices: A Comparative Analysis with GPH Test and Daubechies Wavelets|
|Keywords:||Long-term memory; Wavelets; Stock prices; GPH test|
|Subjects:||C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics
G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
|Depositing User:||Atilla Cifter|
|Date Deposited:||02. Apr 2007|
|Last Modified:||12. Feb 2013 16:03|
Barkoulas, J.T. & Baum, C.F., (1996) "Long-term dependence in stock returns," Economics Letters, 53(3) : 253-259.
Bayraktar, E, Poor H.V. and Sircar, K.R., (2003) “Estimating the Fractal Dimension of the S&P 500 Index Using Wavelet Analysis”, Working Paper, Department of Electrical Engineering, Princeton University, 2003.
Cifter, A. and Chambers, N., (2006) “Testing Fractional Integration of Forward Rat Unbiasedness Hypothesis: Evidence from Turk DEX”, Proceeding of the Internatıonal Fınance Symposıum, Marmara University, 2006.
Crowley, P., (2005) "An intuitive guide to wavelets for economists," Research Discussion Papers Bank of Finland, 1/2005.
Daubechies, I., (1988) “Ortonormal bases of compactly supported wavelets”, Communications on Pure and Applied Mathematics, 41: 909-996
Devore, R., Jawerth, B. and Popov, V., “Compression of wavelet decompositions”, American Journal of Mathematics, 114:737-785.
Gencay, R., Seluk, F., Whitcher, B. (2002) “An Introduction to Wavelets and Other Filtering Methods in Finance and Economics”, Academic Press.
Geweke, J., and Porter-Hudak, S. (1983), “The estimation and application of long memory time series models”, Journal of Time Series Analysis, 4: 221–238.
Granger, C.W.J. and Joyeux, R. (1980) “An Introduction to Long Memory Time Series Models and Fractional Differencing”, Journal of Time Series Analysis 1: 15-29.
Hardle,W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (1998) “Wavelets, Approximation, and Statistical Applications”, Springer, New York.
Hosking, J. R., (1981) “Fractional differencing”, Biometrika, 68: 165–176.
Hurst, H. E. (1951) “Long Term Storage of Reservoirs”, Transactions of the American Society of Civil Engineers, 116: 770-799
Jensen, M. J., (1999) “Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter”, Journal of Forecasting, 18: 17–32.
Jensen, M.J. (2000) “An Alternative Maximum Likelihood Estimator of Long-Memory Processes Using Compactly Supported Wavelets”, Journal of Economic Dynamics and Control 24: 361—387.
Jensen, M.J. and Whitcher, B. (2000) “Time-Varying Long-Memory in Volatility: Detection and Estimation with Wavelets”, Technical report, University of Missouri and EURANDOM.
Jin, Hyun J., Elder, J., Koo, W.W., (2006) "A reexamination of fractional integrating dynamics in foreign currency markets," International Review of Economics & Finance, 15(1): 120-135
Kasman, A. Kirbas, K.B. and Turgutlu, E. (2005) “Nominal and Real Convergence Between the CEE Countries and the EU: A Fractional Cointegration Analysis", Applied Economics, 37: 2487-2500
LeRoy, S.F. (1989) “Efficient Capital Markets and Martingales”, “Journal of Economic Literature”, 1583-22.
Maheswaran S., (1990), "Predictable Short-Term Variation in Asset Prices: Theory and Evidence," Working Paper, Carlson School of Management, University of Minnesota
McCoy, E. J., and A. T. Walden. (1996). “Wavelet analysis and synthesis of stationary long-memory processes” Journal of Computational and Graphical Statistics, 5: 1–31.
Nason, G.P. and von Sachs, R. (1999) “Wavelets in Time Series Analysis”, Philosophical Transactions of the Royal Society of London, Series A 357, 2511-2526.
Percival, D.B. and Walden, A.T. (2000) “Wavelet Methods for Time Series Analysis”, Cambridge University Press.
Schleicher, C. (2002) “An Introduction to Wavelets for Economists”, Monetary and Financial Analysis Department, Bank of Canada, Working Paper 2002-3.
Sowell, F. (1990). “The fractional unit root distribution.” Econometrica, 58: 495–505.
Tevfik, A. H., and M. Kim. (1992). “Correlation structure of the discrete wavelet coefficients of fractional Brownian motion.” IEEE Transactions on Information Theory, 38: 904–909.
Tkacz, G., (2001) “Estimating the Fractional Order of Integration of Interest Rates Using a Wavelet OLS Estimator”, Studies in Nonlinear Dynamics&Econometrics, 5 (1).
Vuorenmaa, T. (2004) “A Multiresolution Analysis of Stock Market Volatility Using Wavelet Methodology”, Licentiate Thesis, University of Helsinki.
Whitcher, B. and Jensen, M.J. (2000) “Wavelet Estimation of a Local Long Memory Parameter”, Exploration Geophysics, 31: 94-103.
Wornell, G. W. and Oppenheim, A. V. (1992), "Estimation of Fractal Signals from Noisy Measurements Using Wavelets", IEEE Trans. Signal Processing, 40:3.