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Econometrics 2015, 3(2), 265-288; doi:10.3390/econometrics3020265

Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

Department of Mathematics, University of Bergen, 5020 Bergen, Norway
Author to whom correspondence should be addressed.
Academic Editor: Timo Teräsvirta
Received: 26 November 2014 / Revised: 27 March 2015 / Accepted: 2 April 2015 / Published: 14 April 2015
(This article belongs to the Special Issue Non-Linear Regression Modeling)
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This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is the number of regenerations for a \(\beta\)-null recurrent process and the limiting distribution (with proper normalization) is normal. Furthermore, we show that the two-step estimator for the volatility function is consistent. The finite sample performance of the estimate is quite reasonable when the leave-one-out cross validation method is used for bandwidth selection. We apply the proposed method to study the relationship of Federal funds rate with 3-month and 5-year T-bill rates and discover the existence of nonlinearity of the relationship. Furthermore, the in-sample and out-of-sample performance of the nonparametric model is far better than the linear model. View Full-Text
Keywords: β-null recurrent; cointegration; conditional heteroscedasticity; Markov chain; nonparametric regression β-null recurrent; cointegration; conditional heteroscedasticity; Markov chain; nonparametric regression

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cai, B.; Tjøstheim, D. Nonparametric Regression Estimation for Multivariate Null Recurrent Processes. Econometrics 2015, 3, 265-288.

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