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In this paper, Using the daily stock return data, we show that Shanghai stock market prices exhibit long memory process, and estimate the long-memory parameters by wavelet. Using the sparse wavelet representation of a matrix operator, we are able to approximate an ARFIMA models likelihood function with the series’s wavelet coefficients and their variances. Maximization of this approximate likelihood function over the long memory parameter space resu1ts in the approximate wavelet maximum likelihood estimates of the ARFIMA model.
Use this daily stock market prices exhibit long memory process, and estimate the long-memory parameters by wavelet. Using the sparse wavelet representation of a matrix operator, we are able to approximate an ARFIMA models likelihood function with the series of wavelet coefficients and their variances. Maximization of this approximate likelihood function over the long memory parameter space resu1ts in the approximate wavelet maximum likelihood estimates of the ARFIMA model.