A brief survey on the choice of parameters for: “Kernel density estimation for time series data”

Abstract

This paper presents an overview of the empirical performance of some of the common methods for parameter selection in the area of enhanced dynamic kernel density and distribution estimation with exponentially declining weights. It is shown that exponential weighting delivers accurate nonparametric density and quantile evaluations, without common corrections for scale and/or location in most of the financial time series considered, provided that parameters are chosen appropriately with computationally heavy Least-Squares routines. For more time-efficient numerical optimisations and/or simple kernel adaptive estimation strategies, Least-Squares routines may be re-written with exponentially weighted binned kernel estimators. This insures equally effective parameters evaluation under the different choices of kernel functional forms, though binning strategy becomes an important component of estimations. On the other hand, it is also highlighted that if the estimations target is to mine time-varying nonparametric quantiles, kernel functional forms and bandwidths may not be necessary for these evaluations. Combining exponential weights with empirical distribution estimator provides a very similar quantile performance to the kernel enhanced estimator, while parametric specifications may provide a better extreme quantiles outlook.