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MULTIVARIATE AR SYSTEMS AND MIXED FREQUENCY DATA: G-IDENTIFIABILITY AND ESTIMATION

Published online by Cambridge University Press:  02 April 2015

Brian D.O. Anderson ,
Manfred Deistler ,
Elisabeth Felsenstein ,
Bernd Funovits ,
Lukas Koelbl  and
Mohsen Zamani
Brian D.O. Anderson
Affiliation:
Australian National University and National ICT Australia Ltd.
Manfred Deistler*
Affiliation:
Vienna University of Technology and Institute for Advanced Studies
Elisabeth Felsenstein
Affiliation:
Vienna University of Technology
Bernd Funovits
Affiliation:
University of Vienna and Vienna University of Technology
Lukas Koelbl
Affiliation:
Vienna University of Technology
Mohsen Zamani
Affiliation:
Australian National University
*
*Address correspondence to Manfred Deistler, Institute of Statistics and Mathematical Methods in Economics, Unit: Econometrics and System Theory, Vienna University of Technology, Vienna, Austria; e-mail: deistler@tuwien.ac.at.
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Abstract

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This paper is concerned with the problem of identifiability of the parameters of a high frequency multivariate autoregressive model from mixed frequency time series data. We demonstrate identifiability for generic parameter values using the population second moments of the observations. In addition we display a constructive algorithm for the parameter values and establish the continuity of the mapping attaching the high frequency parameters to these population second moments. These structural results are obtained using two alternative tools viz. extended Yule Walker equations and blocking of the output process. The cases of stock and flow variables, as well as of general linear transformations of high frequency data, are treated. Finally, we briefly discuss how our constructive identifiability results can be used for parameter estimation based on the sample second moments.

Type
ET LECTURE
Information
Econometric Theory , Volume 32 , Issue 4 , August 2016 , pp. 793 - 826
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2015

Footnotes

The authors want to thank Hans Havlicek, Vienna University of Technology, and Benedikt Pötscher, University of Vienna, for valuable suggestions concerning the proof of Theorem 2. In addition we thank Peter Phillips, several anonymous referees and handling co-editors for valuable comments.

Support by the FWF (Austrian Science Fund under contracts P20833/N18 and P24198/N18), the ARC (Australian Research Council under Discovery Project Grant DP1092571) and NICTA is gratefully acknowledged. NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the ARC through the ICT Centre of Excellence program.

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