16 - Future directions

Summary

A chapter on future directions will have several subjective elements. Here we list topics that should be pursued in the future and also mention those topics that should not be pursued in the future.

Nonlinear models

Throughout the book we considered linear models only. Obviously all the topics discussed earlier need to be extended to nonlinear models. Thus, nonlinear error correction, nonlinear cointegration, and nonlinear structural change are possible topics. Some references here are: Granger (1995), Granger and Swanson (1996, 1997), Granger and Terasvirta (1993), and Granger, Inoue, and Norin (1997).

Bootstrap methods

There is currently too much asymptotic theory. Significance levels obtained from asymptotic distributions have been found to be misleading unless samples are very large. As reviewed in chapter 10, bootstrap methods are promising in making inferences with moderate-sized samples. More work needs to be done in this direction.

Robust methods

In chapter 14, we discussed robust unit root tests (section 14.5) and robust estimation methods for cointegrating regressions (section 14.6). Given that many error distributions are nonnormal, more developments of robust methods will be practically useful. Lucas (1995) develops tests for cointegration using pseudo-likelihood methods.

Pre-testing problems

The problems with unit roots and cointegration analysis within the context of linear models are far from solved. Thus, future developments in nonlinear models (as suggested by Granger and Swanson 1996, 1997) maybe premature. One important question that has not even been asked is the appropriate significance levels at which the unit root tests should be applied, when they are pre-tests – prelude to cointegration analysis.