Comparison of Differencing Parameter Estimation Using Spectral Regression for Short Memory Data (Simulation Study)

One of the most common methods used for the estimation of differentiating parameters inthe Long Memory model is spectral regression. The spectral density function of the Long Memory Model isformed into a simple linear regression equation to estimate the parameter d by the least-squares method.This approach has drawn many researchers ' attention because it can solve the problems of reducing theautocovariance function of the Long Memory system. Parameter estimation d by the regression method canbe done directly without knowing the parameters p and q beforehand. This method was first proposed byGeweke and Porter-Hudak (1983) and modified by Reisen (1994) using smooth Periodogramby the ParzenWindow. Then, Robinson (1995) added Trimming l to the Periodogram. Hurvich and Ray (1995) andVelasco (1999a) added the Cosine-Bell taper to the Periodogram, Velasco (1999b) replaced the independentvariable to j, which is the index of the Periodogram. In this study, the accuracy of these methods will becompared to the short memory data (ARIMA) by using a simulation study. In this study, the simulationstudy results show the Geweke and Porter-Hudak (GPH) and Reisen (SPR) methods provide relativelyaccurate results in estimating the parameters d of the long memory model, even for short memory data. Theresults of the comparison show that the GPH and SPR methods are better than the other methods based onthe estimated values of the true value of d (generated) and based on the resulting deviation of thedifferentiating coefficient (d).