Some simple remarks on an autoregressive scheme and an implied problem. (English) Zbl 0895.60039

Rosenblatt, Murray

J. Theor. Probab. 10, No. 2, 295-305 (1997).

Summary: Nonminimum phase autoregressive schemes are considered in the context of the problem of determining a stationary process that satisfies a possibly nonlinear autoregressive system of equations. It is noted that in most solutions there is an implicit assumption that the independent random variables generating the process are independent of the past of the process. This is not true of the nonminimum phase schemes. A simple scheme that has a characteristic polynomial with roots inside and outside the unit disc in the complex plane is discussed.

MSC:

60G10	Stationary stochastic processes
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

stationary processes; autoregressive system; Markov process