Extended Yule-Walker Identification of VARMA Models with Single- or Mixed-Frequency Data

28 Pages Posted: 9 Jun 2016

See all articles by Peter A. Zadrozny

Peter A. Zadrozny

U.S. Bureau of Labor Statistics - Department of Labor; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: May 2016

Abstract

Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector autoregressive moving-average (VARMA) model with available covariances of single- or mixed-frequency observations on the variables of the model. The paper proves that under conditions of stationarity, regularity, miniphaseness, controllability, observability, and diagonalizability on the parameters of the model, the parameters are determined uniquely with available population covariances of single- or mixed-frequency observations on the variables of the model, so that the VARMA model is identified with the single- or mixed-frequency covariances.

Keywords: block-Vandermonde eigenvectors of block-companion state-transition matrix of state-space representation, matrix spectral factorization

JEL Classification: C320, C800

Suggested Citation

Zadrozny, Peter A., Extended Yule-Walker Identification of VARMA Models with Single- or Mixed-Frequency Data (May 2016). CESifo Working Paper Series No. 5884. Available at SSRN: https://ssrn.com/abstract=2791368

Peter A. Zadrozny (Contact Author)

U.S. Bureau of Labor Statistics - Department of Labor ( email )

2 Massachusetts Avenue, NE
Washington, DC 20212
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

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