New Methods for the Analysis of Long-Memory Time Series

Abstract

Some recent developments in the analysis of time series are applied to real economic data. It is assumed that any stochastic or nonstochastic trends have been removed from the raw observed time series. Models for long-memory time series are considered in which the autocovariance sequence is parameterized only at very long lags or the spectral density is parameterized only at very low frequencies. The recently proposed methods for estimating the differencing parameters are applied to an economic time series of prices in Spain. The results consistently indicate that the inflation series suffers from long memory. The corelogram and periodogram for the resulting filtered series are plotted. The autocorrelation estimates are very close to zero. However, the seasonal peaks are still present