Local Limit Theory and Spurious Nonparametric Regression
Peter C. B. Phillips
Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics
May 1, 2008
Cowles Foundation Discussion Paper No. 1654
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), 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.
Number of Pages in PDF File: 32
Keywords: Brownian motion, Kernel method, Local R² , Local Durbin-Watson ratio, Local time, Integrated process, Nonparametric regression, Spurious regression
JEL Classification: C23, C25working papers series
Date posted: May 21, 2008
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