Density estimation by neural networks: With applications to non-Gaussian distributions in time series analysis

This thesis introduces methods to analyse data prone to uncertainty pronounced in different ways such as volatile observations, erroneous measurements, missing values, outliers, etc. Posing distributional assumptions about the underlying data process, as is custom in econometrics, may result in model misspecification leading to misleading results and incorrect conclusions. Therefore it is of uttermost importance to assess these data before performing trustworthy statistical inference. A fundamental contribution of this thesis is estimating the full distribution of these complex data processes by neural networks. Novel methods are constructed to estimate densities for cross-sectional data, that is collected at a single period in time. Applications are shown for road sensor data which collect vehicle counts passing sensors at different segments of the highway in the Netherlands. By analysing these, the behaviour of traffic can be identified during rush hour for example. Furthermore, novel filtering methods are developed in time series analysis where data is collected at sequential points in time. These are applied to road sensor data to analyse for example traffic behaviour during a whole working day.