Vector Autoregressions with Dynamic Factor Coefficients and Conditionally Heteroskedastic Errors

Tinbergen Institute Discussion Paper 2021-056/III

30 Pages Posted: 8 Jul 2021

See all articles by Paolo Gorgi

Paolo Gorgi

University of Padua; VU University Amsterdam - Faculty of Economics and Business Administration

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Julia Schaumburg

Tinbergen Institute; VU University Amsterdam

Date Written: June 28, 2021

Abstract

We introduce a new and general methodology for analyzing vector autoregressive models with time-varying coefficient matrices and conditionally heteroskedastic disturbances. Our proposed method is able to jointly treat a dynamic latent factor model for the autoregressive coefficient matrices and a multivariate dynamic volatility model for the variance matrix of the disturbance vector. Since the likelihood function is available in closed-form through a simple extension of the Kalman filter equations, all unknown parameters in this flexible model can be easily estimated by the method of maximum likelihood. The proposed approach is appealing since it is simple to implement and computationally fast. Furthermore, it presents an alternative to Bayesian methods which are regularly employed in the empirical literature. A simulation study shows the reliability and robustness of the method against potential misspecifications of the volatility in the disturbance vector. We further provide an empirical illustration in which we analyze possibly time-varying relationships between U.S. industrial production, inflation, and bond spread. We empirically identify a time-varying linkage between economic and financial variables which are effectively described by a common dynamic factor. The impulse response analysis points towards substantial differences in the effects of financial shocks on output and inflation during crisis and non-crisis periods.

Keywords: time-varying parametersvector autoregressive model, dynamic factor model, Kalman filter, generalized autoregressive conditional heteroskedasticity, orthogonal impulse response function

JEL Classification: C32, E31

Suggested Citation

Gorgi, Paolo and Gorgi, Paolo and Koopman, Siem Jan and Schaumburg, Julia and Schaumburg, Julia, Vector Autoregressions with Dynamic Factor Coefficients and Conditionally Heteroskedastic Errors (June 28, 2021). Tinbergen Institute Discussion Paper 2021-056/III, Available at SSRN: https://ssrn.com/abstract=3875604 or http://dx.doi.org/10.2139/ssrn.3875604

Paolo Gorgi (Contact Author)

University of Padua ( email )

Via 8 Febbraio, 2
Padova, Vicenza 35122
Italy

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Julia Schaumburg

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

HOME PAGE: http://juliaschaumburg.com

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands
+31 (0)20 59 82653 (Phone)

HOME PAGE: http://juliaschaumburg.com

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