Essays on time series analysis and statistical machine learning

Abstract

This thesis encompasses three research articles contributing to the fields of time series analysis and statistical machine learning. Firstly, we develop a peaks-over- threshold approach, which captures both short- and long-term correlations in the underlying time series in order to model the clustering behaviour in high-threshold exceedances. The suggested model is motivated by and applied to oceanographic data. Secondly, we propose an efficient discrepancy-based inference approach for intractable generative models based on quasi-Monte Carlo methods. We demonstrate that this method substantially reduces the computational cost of estimating the model parameters in various applications of academic and practical interest. Thirdly, we suggest training methods for deep sequential models, which improve the forecast precision when facing structural breaks in the in-sample period. These mitigation strategies are examined in an extensive simulation study and utilised to forecast energy data. As the developed theory in this thesis is very versatile, it is applicable to a broad range of data types as well as research fields, and in particular to economic time series.