Dynamic Misspecification in Nonparametric Cointegrating Regression

Ioannis Kasparis and Peter C. B. Phillips ()
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Ioannis Kasparis: University of Cyprus

No 1700, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a "pseudo-true function" limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed.

Keywords: Dynamic misspecification; Functional regression; Integrable function; Integrated process; Local time; Misspecification; Mixed normality; Nonlinear cointegration; Nonparametric regression (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2009-06
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Working Paper: Dynamic Misspecification in Nonparametric Cointegrating Regression (2009)
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