Abstract
This chapter introduces the linear regression model used in applied time series analysis to investigate relations among variables. In Section 1.1, the basic tools and assumptions underlying the model are presented; then the chapter shows how to derive point estimates of the parameters using three possible estimation methods, that is, ordinary least square, generalized least squares, and maximum likelihood; moreover, a range of methods to build tests of hypotheses on the parameters are developed. In Section 1.2, the chapter explains how to deal with violations of the hypotheses of the linear regression framework. Section 1.3 deals with the selection of the appropriate regressors and presents some of the issues related with the process of model specification, such as multicollinearity and errors in the measurement of the regressors. Section 1.4 explains how to address potential violations of two initial assumptions on the regression errors of the classical linear regression model, such as heteroskedasticity and autocorrelation. Finally, Section 1.5 provides some intuition on how to interpret the results from an estimated regression.
Keywords: Linear regression; estimation methods; ordinary least squares; generalized least squares; maximum likelihood; tests of hypotheses; confidence intervals; model specification
Essentials of Time Series for Financial Applications 