The Vector Error Correction Index Model: Representation, Estimation and Identification

28 Pages Posted: 4 Apr 2023

See all articles by Gianluca Cubadda

Gianluca Cubadda

University of Rome Tor Vergata - Department of Economics and Finance

Marco Mazzali

University of Rome Tor Vergata

Date Written: April 3, 2023

Abstract

This paper extends the multivariate index autoregressive model by Reinsel (1983) to the case of cointegrated time series of order (1, 1). In this new modelling, namely the Vector Error-Correction Index Model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction w.r.t. the Vector Error Correction Model. We show that the VECIM allows one to decompose the reduced form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.

Keywords: Vector autoregressive models, multivariate autoregressive index model, cointegration, reduced-rank regression, dimension reduction, main business cycle shock

Suggested Citation

Cubadda, Gianluca and Mazzali, Marco, The Vector Error Correction Index Model: Representation, Estimation and Identification (April 3, 2023). CEIS Working Paper No. 556, Available at SSRN: https://ssrn.com/abstract=4408771 or http://dx.doi.org/10.2139/ssrn.4408771

Gianluca Cubadda (Contact Author)

University of Rome Tor Vergata - Department of Economics and Finance ( email )

Via Columbia n.2
Roma, 00133
Italy

Marco Mazzali

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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