Nonlinear kernel mode-based regression for dependent data

Under stationary $\alpha$-mixing dependent samples, we in this article develop a novel nonlinear regression based on mode value for time series sequences to achieve robustness without sacrificing estimation efficiency. The estimation process is built on a kernel-based objective function with a constant bandwidth (tuning parameter) that is independent of sample size and can be adjusted to maximize efficiency. The asymptotic distribution of the resultant estimator is established under suitable conditions, and the convergence rate is demonstrated to be the same as that in nonlinear mean regression. To numerically estimate the kernel mode-based regression, we develop a modified modal-expectation-maximization algorithm in conjunction with Taylor expansion. A robust Wald-type test statistic derived from the resulting estimator is also provided, along with its asymptotic distribution for the null and alternative hypotheses. The local robustness of the proposed estimation procedure is studied using influence function analysis, and the good finite sample performance of the newly suggested model is verified through Monte Carlo simulations. We finally combine the recommended kernel mode-based regression with neural networks to develop a kernel mode-based neural networks model, the performance of which is evidenced by an empirical examination of exchange rate prediction.