Aims and objectives

The aim of this course is to provide an introduction to factor models in time series analysis by teaching students the basic theoretical foundations and by illustrating  them some applications to macroeconomics and finance.

In the last years large datasets have become increasingly available to researchers and practitioners in many disciplines. In particular, during this big data revolution the analysis of high-dimensional time series has become one of the most active subjects of modern statistical methodology with applications in the most different areas of science including finance, econometrics, meteorology, genomics, chemometrics, complex physics simulations, biological and environmental research. Although the value of information is unquestionable, the possibility of extracting meaningful and useful information out of this large amount of data is also of great importance. To achieve such dimension reduction, several new analytical and computational techniques have been developed under the name of machine learning methods. Among these factor models not only are one of the pioneering methods in the field of unsupervised learning (dating back to Spearman, 1904), but up to these days have also been one of the most popular and most employed ones.

We start by discussing principal component analysis as a useful dimension reduction technique for large panels of time series. This is the most simple example of factor model (the static model) which we then generalize to include all temporal relations among the considered variables (the dynamic model). We then focus on the case in which the dynamic model can be re–written as a state space model and we present its estimation via Kalman filter and the Expectation Maximization algorithm. We then consider application of these models in two fields. First, in macroeconometrics for building indicators of the business cycle, for nowcasting, and for policy analysis problems. Related to these we briefly discuss how to deal with the issues of non–fundamentalness and cointegration. Second, in financial econometrics for volatility modelling and forecasting. Related to these we briefly discuss the complementarity of factor and network models and the issue of conditional heteroskedasticity. Real–data applications taken from existing papers are discussed during the lectures. Matlab or R code will be provided.