Application of Regression Modeling to Data Observed Over Time

Abstract

The central idea of this text is to guide researchers through the application of regression modeling when the data under analysis are observed over time. In general, there are no doubts regarding the application of this modeling in cross sections. However, when there is dependence on the data over time, some care needs to be taken for the results to be reliable and have the same interpretation of the coefficients obtained using the least squares method. The text begins with a presentation of the concept of autocorrelation and partial autocorrelation to identify and apply autoregressive modeling. Following this approach, the Augmented Dickey-Fuller test for detecting stationarity is presented, an essential condition for the estimators of ordinary least squares to be consistent. The Granger causality test is also presented and an example of regression applied to the series of the Cost of Living Index and the National Price Index for General Consumers. All the examples are presented with the help of Microsoft Excel to universalize the technique.

Keywords: Longitudinal data; Stationarity; Autoregressive models; Granger causality; Lag

JEL Classification: M00, M1, M2, M21, M10