LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION

Peter C. B. Phillips ()

Econometric Theory, 2009, vol. 25, issue 06, pages 1466-1497

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 R2 and a local Durbin 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.

Date: 2009

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Related works:
Working Paper: Local Limit Theory and Spurious Nonparametric Regression (2008)
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