Local Limit Theory and Spurious Nonparametric Regression

Peter Phillips

No 1654, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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), 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: Brownian motion; Kernel method; Local R^2; Local Durbin-Watson ratio; Local time; Integrated process; Nonparametric regression; Spurious regression (search for similar items in EconPapers)
JEL-codes: C23 C25 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2008-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Published in Econometric Theory (2009), 25: 1466-1497

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Journal Article: LOCAL LIMIT THEORY AND SPURIOUS NONPARAMETRIC REGRESSION (2009)
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