Quantifying the Effect of Sampling Variation in Frequentist Distributional Forecasts in State Space Models

In this thesis we analyse the effect on random sampling variation on distributional forecasts and values extracted from those distributional forecasts, in a particular statistical context. Particular focus was paid to financial applications, particularly in banking, where we analysed how random sampling variation affects estimation of the size of a 1-in-100-day loss required to be calculated daily by banking institutions, and whether sampling variation alone can lead to failure of tests of models imposed by financial regulators and on the interplay between sampling variation and model selection on statistical model performance.