# Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

Biqing Cai () and Dag Tjøstheim ()
Biqing Cai: Department of Mathematics, University of Bergen, 5020 Bergen, Norway
Dag Tjøstheim: Department of Mathematics, University of Bergen, 5020 Bergen, Norway

Econometrics, 2015, vol. 3, issue 2, 1-24

Abstract: 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.

Keywords: β-null recurrent; cointegration; conditional heteroscedasticity; Markov chain; nonparametric regression (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2015
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