MATRIX PARAMETER ESTIMATION IN AN AUTOREGRESSION MODEL

A. P. YURACHKIVSKY AND D. O. IVANENKO

Theory of Stochastic Processes Vol. 12 (28), no. 1–2, 2006, pp. 154–161

The vector difference equation $\xi_k=Af(\xi_{k-1})+\varepsilon_k$,where $(\varepsilon_k)$ is a square integrable difference martingale, is considered. A family of estimators $\check{A}_n$ depending, besides the sample size $n$, on a bounded Lipschitz function is constructed. Convergence in distribution of $\sqrt{n}(\check{A}_n-A)$ as $n\rightarrow\infty$ is proved with the use of stochastic calculus. Ergodicity and even stationarity of $(\varepsilon_k)$ is not assumed, so the limiting distribution may be, as the example shows, other than normal.

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