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Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

Department of Mathematics, University of Bergen, 5020 Bergen, Norway
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Academic Editor: Timo Teräsvirta
Econometrics 2015, 3(2), 265-288; https://doi.org/10.3390/econometrics3020265
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)
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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Cai, B.; Tjøstheim, D. Nonparametric Regression Estimation for Multivariate Null Recurrent Processes. Econometrics 2015, 3, 265-288.

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