Discrete Wavelet Transform and Long Memory in Stock Market Prices
44 Pages Posted: 19 Jun 2002
The discrete wavelet transform is applied to the fractional differencing processes to estimate the long memory parameter by establishing a log-linear relationship between the variance of the wavelet coefficient from the long-memory process and the scaling parameter. The wavelet analysis can remove both the dense covariance matrix the GPH semiparametric method and the MLE create and the disadvantage of Fourier analysis that frequency information can only be extracted for the complete duration of a signal function. The wavelet OLS estimator yields a consistent estimator of the fractional differencing parameter. All the composite stock indices of the Dow Jones, Nasdaq, S&P 500, FTSE, Dax, Mib 30 and Korea's Kospi have found to be generated by the fractional differencing process. These findings are robust because the values were estimated based on the Daubechies wavelet and scaling filters of different widths, the least asymmetric wavelet and scaling filters of different widths, and the coiflet wavelet and scaling filters of width 6.
Suggested Citation: Suggested Citation