Tall Transfer Functions, Singular Spectra and Econometric Modelling

Abstract

Central banks and funds investment managers work with mathematical models. In recent years, a new class of model has come into prominence—generalized dynamic factor models. These are characterized by having a modest number of inputs, corresponding to key economic variables and industry-sector-wide variables for central banks and funds managers respectively, and a large number of outputs, economic time series data or individual stock price movements for example. It is common to postulate that the input variables are linked to the output variables by a finite-dimensional linear time-invariant discrete-time dynamic model, the outputs of which are corrupted by noise to yield the measured data. The key problems faced by central banks or funds managers are model fitting given the output data (but not the input data), and then using the model for prediction purposes. 

These are essentially tasks usually considered by those practicing identification and time series modelling. Nevertheless there is considerable underlying linear system theory. This flows from the fact that the underlying transfer function matrix is tall. This presentation will describe a number of consequences of this seemingly trivial fact, and then go on to indicate how to cope with time series with different periodicities, e.g. monthly and quarterly, where multirate signal processing and control concepts are of relevance.