Estimation of nonstationary ARMAX models based on the Hannan-Rissanen method. (English) Zbl 0721.62091

Huang, Dawei; Guo, Lei

Ann. Stat. 18, No. 4, 1729-1756 (1990).

The authors study estimation problems of orders and coefficients of linear feedback control systems, described by ARMAX models. The algorithms are inspired by the Hannan-Rissanen method for estimation of stationary ARMA models. Almost sure convergence of the estimates is proved using limit theorems for double array martingales and non-negative supermartingales.

Reviewer: H.Dehling (Groningen)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
93E12	Identification in stochastic control theory
60F15	Strong limit theorems

Keywords:

stochastic Lyapunov functions; nonstationary; least squares; order estimation; positive real; coefficients of linear feedback control systems; ARMAX models; Hannan-Rissanen method; Almost sure convergence; double array martingales; non-negative supermartingales