Robust Nonstationary Regression

Peter Phillips

No 1064, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed which allow for endogeneities in the nonstationary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estimators involve semiparametric corrections to accommodate these possibilities and they belong to the same family as the fully modified least squares (FM-OLS) estimator of Phillips and Hansen (1990). Specific attention is given to fully modified least absolute deviation (FM-LAD) estimation and fully modified M (FM-M)-estimation. The criterion function for LAD and some M-estimators is not always smooth and the paper develops generalized function methods to cope with this difficulty in the asymptotics. The results given here include a strong law of large numbers and some weak convergence theory for partial sums of generalized functions of random variables. The limit distribution theory for FM-LAD and FM-M estimators that is developed includes the case of finite variance errors and the case of heavy-tailed (infinite variance) errors. Some simulations and a brief empirical illustration are reported.

Keywords: FM-LAD estimator; FM-M estimator; generalized functions of random variables; laws of large numbers and weak convergence for generalized functions; non-Gaussian nonstationarity; regular sequence; robust estimation (search for similar items in EconPapers)
Pages: 49 pages
Date: 1993-11
Note: CFP 912.
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Published in Econometric Theory (1995), 11: 912-951

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