Kernel Estimation for the Mode and Quantiles of Time Series

In this book, we are interested in the area of nonparametric prediction of time series. Therefore, the relationship between a current observation and past observations is considered, where the conditional density function plays an important role. Two aspects of the conditional probability density function, the mode and the quantiles are studied. Firstly, in the case of the mode, we state some sufficient conditions under which the joint kernel estimator of the conditional mode taken jointly at a finite number of distinct points is asymptotically normally distributed. Secondly, a new multivariate estimator for a multivariate conditional quantile is proposed, based on the reweighted Nadaraya-Watson estimator for the conditional cumulative distribution function. The efficiency of the proposed estimator is tested by giving two applications. The book also, involves a review which covers in sufficient details the up to date literature on kernel estimation for conditional mode and quantiles.