Time-Dependent Time Series Models: Comments on Marc Hallin’s Early Contributions and a Pragmatic View on Estimation

In this chapter, we provide a survey of Marc Hallin’s early contributions to time series analysis. These contributions, which go back to the years 1980s, predate his interest in panel data and high-dimensional dynamic models. We begin with his presentation of causality and (classical) invertibility for VARMA models with time-dependent coefficients (tdVARMA models). Then, we present the generalized Yule-Walker equations that he developed with Ingenbleek for tdVAR models, together with their solution of the model-building problem for these models. Turning to tdVMA models, we sketch the model-building problem and discuss the concept of generalized invertibility. Finally, we comment and extend Marc Hallin’s results and exploit the tdVAR(1) representation one step further to estimate tdVARMA models.