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LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION

Published online by Cambridge University Press:  01 December 2009

Peter C.B. Phillips
Peter C.B. Phillips*
Affiliation:
Yale University, University of Auckland, University of York and Singapore Management University
*
*Address correspondence to Peter C.B. Phillips, Department of Economics, Yale University, P.O. Box 208268, New Haven, CT 06520–8268, USA; e-mail: peterphillips@yale.edu.
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Abstract

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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 R2 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 R2 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.

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ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009, pp. 1466 - 1497
Copyright
Copyright © Cambridge University Press 2009

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