Stationary Time Series

This chapter deals with different features of the data generating process (DGP) of a time series in a univariate framework. The DGP of a time series may be autoregressive (AR), moving average (MA), or a mix of both. AR process could be interpreted as an aggregation of the entire history of innovations. MA process arises from the fact that a time series is obtained by applying the weights to the white noise innovations and then moving the weights and applying them to the series of innovations one period ahead to get the time series one period ahead. The features of these processes have been discussed in detail. Autocorrelation function (ACF) and partial autocorrelation function (PACF) are very much powerful in analysing the stochastic process of a time series. We analyse the shapes of the ACF and PACF of different types of the data generating process. The estimation of ACF and PACF is illustrated by using Stata software with time series data taken from National Accounts Statistics in India.