Using Spectral Density Function in Analysis of Stationary Time Series

Abstract

A useful tool for stationary time series analysis is periodogram. Most economic time series presents a general trend, consequently they are nonstationary. But, through the elimination of this trend there is obtained a stationary series. Testing the stationarity of series is achieved in this paper through Bartlett test. In analysis of stationary series, we used the spectral density function, which is defined through the Fourier series representation and the auto covariance function. The typical stationary time series are: the pure white noise time series, the seasonal processes and the autoregressive processes. The periodogram is obtained through the sample spectral density function. The periodogram is used to study the periodic behavior of the data. In the last part, there are characterized autoregressive processes with order one and two.