Abstract
This chapter illustrates the (univariate) linear time series analysis based on the principle that past information may be used to forecast future realizations of a time series. Section 2.1 defines essential concepts such as stationarity, sample autocorrelation, and partial autocorrelation functions. Then, Section 2.2 presents three alternative linear time series models, that is, the moving average (MA) model, the autoregressive (AR) model, and a combination of the two, called autoregressive moving average (ARMA) process. Section 2.3 illustrates how to select, estimate, and assess the adequacy for a given data set of these models using the procedure proposed by Box and Jenkins (1976). Finally, Section 2.4 shows how to use these alternative models in forecasting applications.
Keywords: Univariate linear time series; autoregressive coefficients; autoregressive models; moving average models; stationarity; forecasting
Essentials of Time Series for Financial Applications 