This chapter is an introduction to econometrics with time series data. Chapters 1 to 4 have been restricted to cross sectional data, data for individuals, firms, countries and so on. Working with time series data will introduce new problems, the first and most important being that time series data may be nonstationary which may lead to spurios (misleading) results. However, this chapter will only look at stationary time series data. Time series models may be static or dynamic, where the latter maeans that the dependent variable may depend on values from previous periods. We will look at some dynamic models, most importantly ADL (autoregressive distributed lag) models and AR (autoregressive) models. Another problem with time series data is that the error terms may be correlated over time (autocorrelation). The chapter concludes with a discussion of autocorrelation, how to test for autocorrelation and how to estimate models in the presence of autocorrelation.
Static time series models
With time series data it is no longer reasonable to assume that our sample is a random sample. For example, inflation in this period tends to be correlated with inflation in the previous period. Instead, it may be reasonable to assume that our time series data is stationary. In this section you will learn more about the stationary the assumption. We also need to modify the Gauss Markov assumptions such that OLS is unbiased, consistent and efficient under these assumptions.
In this section we move onto dynamic time series models. By that we mean that we allow for lagged variables, the value of a variable from an earlier period. We may use lagged explanatory variables as well as lags of the dependent variable as additional explanatory variables. Such a model is called an autoregressive distributed lag model. We will then more carefully study a special case and a simpler model, namely the autoregressive model of order one. This is a simple model where the dependent variable depends on its value in the previous period and an error term. We extend this model to a more general autoregressive model where the dependent variable may depend on its value p periods back in time. We are then ready to go back and discuss estimation of the more general ADL model and we can identify the long run and the short run effects of a change in one of the explanatory variables.
By autocorrelation in a regression model, we mean that the error term in this period depends on its value in previous periods. We will begin by looking at the Breusch-Godfrey test for autocorrelation. If we find that autocorrelation is present then the standard errors from OLS are no longer useful and we will look at robust standard errors. If it can be assumed that the error terms follow an AR(1) process, then it is possible to replace OLS with an efficient estimator.