Common Feature Analysis of Economic Time Series: An Overview and Recent Developments

Abstract

In this paper we overview the literature on common features analysis of economic time series. Starting from the seminal contributions by Engle and Kozicki (1993) and Vahid and Engle (1993), we present and discuss the various notions that have been proposed to detect and model common cyclical features in macroeconometrics. In particular, we analyze in details the link between common cyclical features and the reduced-rank regression model. We also illustrate similarities and differences between the common features methodology and other popular types of multivariate time series modelling. Finally, we discuss some recent developments in this area, such as the implications of common features for univariate time series models and the analysis of common autocorrelation in medium-large dimensional systems.

Dimension Reduction for High Dimensional Vector Autoregressive Models

“…In view of Equation ( 14), it is easy to see that the GLS estimator (15) is the QML estimator of parameters α, conditionally on A, in Model (11). The relation, in terms of efficiency, between the estimators ( 13) and ( 15) is provided in the following theorem.…”

“…Moreover, it implies that the marginal processes of series Y t follow parsimonious univariate models, thus solving the so-called autoregressivity paradox (Cubadda et al, 2009). See Centoni and Cubadda (2015) for a survey. In the analysis that follows, we focus on the case where n is large, virtually with a similar magnitude as the sample size T , whereas r is small compared to T .…”

Dimension Reduction for High‐Dimensional Vector Autoregressive Models*

“…Moreover, it implies that the marginal processes of series $$$ {Y}_t $$$ follow parsimonious univariate models, thus solving the so‐called autoregressivity paradox (Cubadda et al ., 2009). See Centoni and Cubadda (2015) and Cubadda and Hecq (2022) for recent surveys. In the analysis that follows, we focus on the case where $$$ n $$$ is large, virtually with a similar magnitude as the sample size $$$ T $$$, whereas $$$ r $$$ is small compared with $$$ T $$$.…”

Reduced Rank Regression Models in Economics and Finance

“…In this section we review in more details the most common specifications of the RRR approach for the analysis of economic and financial variables. The first two subsections follow and update Centoni and Cubadda (2015) in reviewing models that are mainly applied in macroeconometrics whereas the last subsection focuses on the use of RRR in financial econometrics.…”