Estimation of a matrix-valued parameter of an autoregressive process with nonstationary noise
Authors:
A. P. Yurachkivskiĭ and D. O. Ivanenko
Translated by:
V. Zayats
Journal:
Theor. Probability and Math. Statist. 72 (2006), 177-191
MSC (2000):
Primary 62F12; Secondary 60F05
DOI:
https://doi.org/10.1090/S0094-9000-06-00675-2
Published electronically:
September 6, 2006
MathSciNet review:
2168147
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Abstract: Suppose that $\check {A}_n$ is the least squares estimator constructed from $n$ observations of an unknown matrix $A$ in an autoregressive process $\xi _{k}=A\xi _{k-1}+\varepsilon _{k}$. Under the assumption that the sequence $(\varepsilon _k)$ is a martingale difference, not necessarily stationary and ergodic, we find the limit distribution as $n\to \infty$ of the statistic $\sqrt {n}(\check {A}_{n}-A)$ by using methods of stochastic analysis. This limit distribution may be different from the normal distribution.
References
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References
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Additional Information
A. P. Yurachkivskiĭ
Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, Taras Shevchenko National University, Glushkov Ave. 2, Building 5, 03127 Kyïv, Ukraine
Email:
yap@univ.kiev.ua
D. O. Ivanenko
Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, Taras Shevchenko National University, Glushkov Ave. 2, Building 5, 03127 Kyïv, Ukraine
Email:
ida@univ.kiev.ua
Received by editor(s):
May 24, 2004
Published electronically:
September 6, 2006
Article copyright:
© Copyright 2006
American Mathematical Society