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Nonparametric Regression Estimation for Multivariate Null Recurrent Processes

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  • Biqing Cai

    (Department of Mathematics, University of Bergen, 5020 Bergen, Norway)

  • Dag Tjøstheim

    (Department of Mathematics, University of Bergen, 5020 Bergen, Norway)

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.

Suggested Citation

  • Biqing Cai & Dag Tjøstheim, 2015. "Nonparametric Regression Estimation for Multivariate Null Recurrent Processes," Econometrics, MDPI, vol. 3(2), pages 1-24, April.
  • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:2:p:265-288:d:48167
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    References listed on IDEAS

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