Suppose a time series {Yt} is generated by a first-order stationary self-exciting threshold autoregressive (SETAR) model with Gaussian innovations. The minimum mean squared error h-step ahead forecast for h> 2 involves a sequence of complicated numerical integrations and closed-form expressions are very difficult or even impossible to obtain. In this paper we derive explicit approximate expressions for E[Yt+hYs; s [less-than-or-equals, slant] t] and Var[Yt+hYs; s [less-than-or-equals, slant] t] (h> 2) for various SETAR models. The approximations are reasonably accurate as compared with alternative methods based on numerical integration and Monte Carlo experiments.
[1]
Hung Man Tong,et al.
Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21
,
1983
.
[2]
John. Pemberton.
EXACT LEAST SQUARES MULTI‐STEP PREDICTION FROM NONLINEAR AUTOREGRESSIVE MODELS
,
1987
.
[3]
The busy period of order n in the GI/D/∞ queue
,
1984
.
[4]
H. Tong.
Non-linear time series. A dynamical system approach
,
1990
.
[5]
J. A. Lane,et al.
FORECASTING EXPONENTIAL AUTOREGRESSIVE MODELS OF ORDER 1
,
1989
.
[6]
J. Petruccelli,et al.
A threshold AR(1) model
,
1984,
Journal of Applied Probability.