A RANDOM PARAMETER PROCESS FOR MODELING AND FORECASTING TIME SERIES

Deborah A. Guyton, Nien‐Fan Zhang and Robert V. Foutz

Journal of Time Series Analysis, 1986, vol. 7, issue 2, 105-115

Abstract: Abstract. A generalized autoregressive (GAR) process {Z(t); t = 0, ±1, …} is defined to satisfy the recurrence relation Z(t) = Aθ (t)Z (t ‐l)+ u(t), where {Aθ(t); t = 0,±1, …} is itself a stochastic process depending on a vector parameter θ and where {u(t); t= 0, ±1, …} is white noise with Eu2 (t) =a2. This paper develops theory and methodology and implementing the class of GAR processes for time series modeling and forecasting. Conditions on the ‘parameter process’{Aθ (t); t= 0, ±1, …} are obtained for the existence of a GAR process; necessary and sufficient conditions on {Aθ (t); t= 0, ±1, …} for existence of a stationary GAR process are also obtained. Procedures are developed for computing maximum likelihood estimates of the parameters 0 and u2 and for computing the minimum mean squared error forecasts for GAR processes.

Date: 1986
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