Time Series: Forecasting and Evaluation Methods With Concentration On Evaluation Methods for Density Forecasting

The main focus of this thesis are density forecasts and the corresponding evaluation methods. A density forecast is an estimate of the probability density of predicted values. Density forecasts and the related evaluation methods have been little explored compared to point and interval forecasts, therefore we have chosen to focus on this topic. We go through a detailed description of three evaluation methods for density forecasts. To measure the performance of two of the density forecast evaluation methods we perform a Monte Carlo simulation. We simulate data sets with different data generating mechanisms to measure the size and power for the chosen evaluation methods. Based on our results from the Monte Carlo simulation, we continue with one evaluation method and apply it on empirical data, more specifically on economical, financial and insurance time series data