Regression models with seasonally integrated and possibly endogenous regressors and serially correlated regression errors are studied. Spectral decompositions of generalized sums of cross products of regressors and regression errors are used to develop a feasible generalized least squares estimator (FGLSE) which does not require parametric specifications for error processes. Using the FGLSE and following the spirit of "Fully Modified estimation" of Phillips and Hansen (Rev. Econ. Stud. 57 (1990) 99), a fully modified GLSE (FM-GLSE) and inference procedures are constructed. The distribution of the FM-GLSE is shown to be asymptotically a mixed normal distribution which validates standard inference based on the FM-GLSE with normal theory. A Monte-Carlo simulation shows that the FM-GLSE is more efficient than the ordinary least squares estimator (OLSE) in the cases of endogeneity or serial correlation and more efficient than the FM-estimator based on the OLSE in the case of serial correlation.
Bibliographical noteFunding Information:
The authors are very grateful to the three anonymous referees, an associate editor, and Professor B.U. Park for their helpful comments which lead to significant improvement of the paper. This work was supported by Korea Research Foundation grant KRF- 2002-070-C0001.
- Fourier coefficients
- Semiparametric estimation
- Spectral decomposition