Time Series Regression and ARIMA Models

Abstract

In Chapter 1, we introduced autocorrelation and cross-correlation functions (ACF’s and CCF’s) as tools for clarifying relations that may occur within and between time series at various lags. In addition, we have explained how to build linear models based on classical regression theory for exploiting the associations indicated by large values of the ACF or CCF. The time domain methods of this chapter, contrasted with the frequency domain methods introduced in later chapters, are appropriate when we are dealing with possibly nonstationary, shorter time series; these series are the rule rather than the exception in applications arising in economics and the social sciences. In addition, the emphasis in these fields is usually on forecasting future values, which is easily treated as a regression problem. This chapter develops a number of regression techniques for time series that are all related to classical ordinary and weighted or correlated least squares.