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Theory of Probability and Mathematical Statistics

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Estimation and inference of the vector autoregressive process under heteroscedasticity


Authors: T. Bodnar and T. Zabolotskyy
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 27-45
MSC (2010): Primary 62H12, 62M15; Secondary 62H10
DOI: https://doi.org/10.1090/S0094-9000-2012-00839-9
Published electronically: February 2, 2012
MathSciNet review: 2768846
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Abstract: In this paper we derive the asymptotic distribution of the estimator for the parameters of the vector autoregressive process of order $ p$ with an unconditionally heteroscedastic error process. The covariance matrix of the error process is modeled as a deterministic matrix function and it is estimated nonparametrically at each time point. This estimator is used for deriving inference procedures for the parameters of the vector autoregressive process.


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Additional Information

T. Bodnar
Affiliation: Department of Statistics, European University Viadrina, PO Box 1786, 15207 Frankfurt (Oder), Germany
Email: bodnar@euv-frankfurt-o.de

T. Zabolotskyy
Affiliation: Department of Statistics, European University Viadrina, PO Box 1786, 15207 Frankfurt (Oder), Germany
Email: zabolotskyy@euv-frankfurt-o.de

DOI: https://doi.org/10.1090/S0094-9000-2012-00839-9
Keywords: Heteroscedasticity, inference procedure, parameter estimation, vector autoregressive process
Received by editor(s): October 5, 2009
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society