d 7/14/99 8:36 PM Page 571
Chapter Eighteen
Advanced Time Series Topics
n this chapter, we cover some more advanced topics in time series econometrics. In Chapters 10, 11, and 12, we emphasized in several places that using time series data Iin regression analysis requires some care due to the trending, persistent nature of many economic time series. In addition to studying topics such as infinite distributed lag models and forecasting, we also discuss some recent advances in analyzing time series processes with unit roots. In Section 18.1, we describe infinite distributed lag models, which allow a change in an explanatory variable to affect all future values of the dependent variable. Conceptually, these models are straightforward extensions of the finite distributed lag models in Chapter 10; but estimating these models poses some interesting challenges. In Section 18.2, we show how to formally test for unit roots in a time series process. Recall from Chapter 11 that we excluded unit root processes to apply the usual asymp- totic theory. Because the presence of a unit root implies that a shock today has a long- lasting impact, determining whether a process has a unit root is of interest in its own right. We cover the notion of spurious regression between two time series processes, each of which has a unit root, in Section 18.3. The main result is that even if two unit root series are independent, it is quite likely that the regression of one on the other will yield a statistically significant t statistic. This emphasizes the potentially serious conse- quences of using standard inference when the dependent and independent variables are integrated processes. The issue of cointegration applies when two series are I(1), but a linear combina- tion of them is I(0); in this case, the regression of one on the other is not spurious, but instead tells us something about the long-run relationship between them. Cointegration between two series also implies a particular kind of model, called an error correction model, for the short-term dynamics. We cover these models in Section 18.4. In Section 18.5, we provide an overview of forecasting and bring together all of the tools in this and previous chapters to show how regression methods can be used to fore- cast future outcomes of a time series. The forecasting literature is vast, so we focus only on the most common regression-based methods. We also touch on the related topic of Granger causality.
571 d 7/14/99 8:36 PM Page 572
Part 3 Advanced Topics
18.1 INFINITE DISTRIBUTED LAG MODELS Let {(yt,zt): t …, 2, 1,0,1,2,…} be a bivariate time series process (which is only partially observed). An infinite distributed lag (IDL) model relating yt to current and all past values of z is