Some asymptotic results of a non-parametric conditional mode estimator for functional time-series data

We consider the estimation of the conditional mode function when the covariates take values in some abstract function space. The main goal of this paper was to establish the almost complete convergence and the asymptotic normality of the kernel estimator of the conditional mode when the process is assumed to be strongly mixing and under the concentration property over the functional regressors. Some applications are given. This approach can be applied in time-series analysis to the prediction and confidence band building. We illustrate our methodology by using El Nino data.