Studies in observation-driven time series models: Theory, methods, and applications

This thesis contributes to the theory, methodology and applications of observation-driven time series models. While the basic observation-driven models are important tools in time series analysis, they may encounter challenges in capturing non-linear relationships. In particular, dynamic relationships are often subject to structural breaks, complex nonlinearities, or other time-varying properties that may require special treatment. Furthermore, the increasing availability of data requires models that can accommodate large-dimensional data sets, while maintaining interpretability and low estimation uncertainty. The following chapters contribute to the literature by addressing these issues. Chapter 2 introduces a novel flexible rolling-window estimator. This estimator is designed to improve the forecasting performance of simple autoregressive models. We show that the features of the window can be fine-tuned using regularization and that, in misspecified model settings, the introduction of weights can improve the forecasting performance of simple dynamic models. In an empirical study, we document the improvements in forecasting accuracy by giving higher weights to observations from past recessions. Chapter 3 introduces a multilevel factor model with observation-driven filters for the dynamic factors. The model aims to summarize the dynamics of time series in a few unobserved factors. This model is suitable for large-dimensional panels of economic time series and allows for interdependence structures across multiple sectors. We introduce a simple and fast estimation procedure based on sequential filtering and regression steps. We apply this model to analyze the role of industrial and non-industrial production sectors in the US economy. Chapter 4 provides an overview of applications and methodological contributions in the literature on score-driven models. In particular, in the context of macroeconomic studies, it reviews the score-driven nonlinear autoregressive, dynamic factor, dynamic spatial, and Markov switching models. In the context of finance studies, it discusses score-driven models for integer-valued time series, multivariate scale, and dynamic copula models. Given the considerable interest in both factor and score-driven models, Chapter 5 introduces a novel score-driven dynamic factor model. We provide a general theoretical framework for this class of models, introduce a novel estimator, and study its theoretical properties. We highlight the empirical usefulness of this model in the construction of indices of economic activity in the presence of V-shaped recessions.