Estimation of matrix autoregression process parameters with nonstationary noise. (Ukrainian, English) Zbl 1121.62076

Yurachkivs’kyj, A. P.; Ivanenko, D. O.

Teor. Jmovirn. Mat. Stat. 72, 158-171 (2005); translation in Theory Probab. Math. Stat. 72, 177-191 (2006).

A matrix autoregression model \(\xi_k=A\xi_{k-1}+\varepsilon_k\) is considered with \(\varepsilon_k\) being a martingale-differences sequence. The least squares estimate for \(A\) is \[ \hat A_n=(\sum_{i=1}^n\xi_i\xi_{i-1}^T) (\sum_{i=1}^n\xi_i\xi_i^T)^{+} \] (\(B^{+}\) being generalized inverse to \(B\)). The asymptotic distribution (maybe non-Gaussian) of \(\sqrt{n}(\hat A_n-A)\) is described. A scalar AR(r) model is considered as an example.

Reviewer: R. E. Maiboroda (Kyïv)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10	Point estimation
62M09	Non-Markovian processes: estimation
62F12	Asymptotic properties of parametric estimators
60F05	Central limit and other weak theorems

Keywords:

martingale-differences innovations; least squares estimate; asymptotic distribution