This chapter presents the following content: Linear versus nonlinear adjustment, simple extensions of the ARMA model, testing for nonlinearity, threshold autoregressive models, extensions of the TAR model, three threshold models, smooth transition models,. | Chapter 7 Applied Econometric Time Series 4rd ed. Walter Enders AETS 3rd. edition 1 1 LINEAR VERSUS NONLINEAR ADJUSTMENT On a long automobile trip to a new location, you might take along a road atlas. For most trips, such a linear approximation is extremely useful. Try to envision the nuisance of a nonlinear road atlas. For other types of trips, the linearity assumption is clearly inappropriate. It would be disastrous for NASA to use a flat map of the earth to plan the trajectory of a rocket launch. Similarly, the assumption that economic processes are linear can provide useful approximations to the actual time-paths of economic variables. Nevertheless, policy makers could make a serious error if they ignore the empirical evidence that unemployment increases more sharply than it decreases. 2 The Use of Nonlinear Models It is now generally agreed that linear econometric models do not capture the dynamic relationships present in many economic time-series. The observation that firms are more apt to raise than to lower prices is a key feature of many macroeconomic models. Neftci (1984), Falk(1986), DeLong and Summers (1988), Granger and Lee (1989), and Teräsvirta and Anderson (1992) establish the result that many real variables display non-linear adjustment over the course of the business cycle. In several papers, Enders and Sandler model many terrorist incident series as nonlinear. However, adopting an incorrect non-linear specification may be more problematic than simply ignoring the non-linear structure in the data. It is not surprising, therefore, that non-linear model selection is an important area of current research. 3 The Interest Rate Spread There is evidence that interest rate spreads (st) display a nonlinear adjustment pattern. As long as | a2 | > | a1 |, periods when st–1 < will tend to be more persistent than other periods. 4 yt-1 yt yt = 1yt-1 -1 +1 } r1 -r1 { r2 Symmetric vs Asymmetric Adjustment 5 6 Autoregressive Moving Average (ARMA) Models The . | Chapter 7 Applied Econometric Time Series 4rd ed. Walter Enders AETS 3rd. edition 1 1 LINEAR VERSUS NONLINEAR ADJUSTMENT On a long automobile trip to a new location, you might take along a road atlas. For most trips, such a linear approximation is extremely useful. Try to envision the nuisance of a nonlinear road atlas. For other types of trips, the linearity assumption is clearly inappropriate. It would be disastrous for NASA to use a flat map of the earth to plan the trajectory of a rocket launch. Similarly, the assumption that economic processes are linear can provide useful approximations to the actual time-paths of economic variables. Nevertheless, policy makers could make a serious error if they ignore the empirical evidence that unemployment increases more sharply than it decreases. 2 The Use of Nonlinear Models It is now generally agreed that linear econometric models do not capture the dynamic relationships present in many economic time-series. The observation that firms .
