The article provides an overview of probabilistic forecasting and discusses a theoretical approach to assessing the quality of density forecasts, based on proper scoring rules and moments. An artificial example of predicting second-order autoregression and an example of predicting RTSI stock...

In this article, we propose a simulation method to implement Hong and Li’s (2005) transition density based test for continuous-time models. The idea is to simulate a sequence of dynamic probability integral transforms, which is the key ingredient of Hong and Li’s (2005) test. The...

A time-varying probability density function, or the corresponding cumulative distribution function, may be estimated nonparametrically by using a kernel and weighting the observations using schemes derived from time series modelling. The parameters, including the bandwidth, may be estimated by...