COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1064 Robust Nonstationary Regression Peter C. B. Phillips November 1993 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. |
