9422922 Peter Phillips Model choice, model simplification and the determination of good models for prediction are all important elements in empirical econometric research. When times series are nonstationary, an aspect of model choice is how to model the nonstationarity of the data (e.g., stochastic trends versus deterministic trends versus trend breaks). Although difficult this choice has a substantial impact on the performance of out-of-sample forecasts and forecast confidence sets. Furthermore, in practical business and financial research we are sometimes faced with the need to model or predict large number of series simultaneously. In such situations we need automated procedures for model selection that can take account such critical aspects of a series as its stationarity or lack thereof. The first of the three projects in this research is concerned with the development and justification of such procedures for use in the analysis of economic time series. The methods employed are Bayesian and build on ideas on model determination, hypothesis testing, and forecasting in the presence of non-stationarity that the PI has put forward in recent research. The second project by the PI looks at kernel regression when the errors are nonstationary. Although kernel regression theory is quite well developed in the stationary time series case, there appears to be no theory for case of unit roots or integrated processes. One problem with kernel regression in this case is that estimators are often inconsistent. The research develops modified kernel estimators that are consistent in the presence of nonstationarity both with and without long memory. The third project is an extension of the PIs work on "fully modified" VAR (FM-VAR) estimators. These estimators can take advantage of potential cointegrating links between series without having to be explicit about their form or dimension and without preliminary testing. This research extends the previous work so as to allow for I(0), I(1) , and I(2) regressors simultaneously in the same VAR. It proceeds without making any specific assumptions about the degree of cointegration or the order of cointegration of any of the regressors, and without pretesting of the cointegrating rank.
