A Monte Carlo Comparison of the Regression Method and the Spectral Methods of Prediction

We consider the question of estimating the linear, least-squares predictor of the future values of a real-valued, discrete, purely nondeterministic, stationary time series from its known past. A method of estimating the prediction coefficients from the usual ‘windowed’ estimates of spectral density function is put forward and a Monte Carlo comparison of this method with the more usual regression method of finding the best fitting autoregressive process by recursively solving the Yule-Walker equations is carried out.