Title

Local Limit Theory and Spurious Nonparametric Regression

Publication Type

Journal Article

Publication Date

12-2009

Abstract

A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of: such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated processes that includes the important practical case of spurious regressions. Some local regression diagnostics are suggested for forensic analysis of such regresssions, including a local R-2 and a local Durbin-Watson (DW) ratio, and their asymptotic behavior is investigated. The most immediate findings extend the earlier work on linear spurious regression (Phillips, 1986, Journal of Econometrics 33, 311-340) showing that the key behavioral characteristics of statistical significance, low DW ratios and moderate to high R-2 continue to apply locally in nonparametric Spurious regression. Some further applications of the limit theory to models of nonlinear functional relations and cointegrating regressions are given. The methods, are also shown to be applicable in partial linear semiparametric nonstationary regression.

Keywords

Integrated Time - series, Econometrics, Asymptotics, Convergence, Sums

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometric Theory

Volume

25

Issue

6

First Page

1466

Last Page

1497

ISSN

0266-4666

Identifier

10.1017/S0266466609990223

Publisher

Cambridge University Press (CUP): HSS Journals

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