Let
Xt be a stochastic process satisfying some conditions. We assume that
EXt=
mt is a periodic function, i.e.,
mt=
mt-s for a positive integer
s. There are many popular predictors for
Xh (0<
h_??_
s) under the observation {
Xt;-(
T-1)_??_
t_??_0}. In this paper, we show some statistical properties of one of these predictors, which we denote _??_
h. The predictor _??_
h is composed of the sum of the least squares estimator _??_
t of
mt, and a linear predictor _??_
h of
Zh=
Xh-
mh, which is obtained by the least squares method. When
Zt is a stationary process, _??_
h is a reasonable predictor. The main point of this paper is to discuss the robustness of _??_
h when
Zt deviates from a stationary process. As a nonstationary process
Zt we consider the case when
∇_??_Zt=
Zt-
Zt-s=
Yt is stationary. We show comparisons between the asymptotic prediction error of _??_
h and that of another predictor when the sample size tends to infinity.
抄録全体を表示