A model for variables with suddenly changing parameters
Ji[rbreve]í And[ebreve]l · Communications in Statistics - Simulation and Computation · 1994
A process Xt= θt+et is investigated in the paper where {θt} is a Markov chain with real states s1,…,sm and {et} is a strict white noise. It is assumed that the off-diagonal elements of the matrix of transition probabilities of the chain {θt} are small. Formulas for forecasting the process {Xt} are given. Two models are investigated in detail: (1)a chain with equal off-diagonal transition probabilities , and (2)a chain with three states. The parameters are estimated by the moment method. Theoretical results are applied to time series describing minimum and maximum Nile's water level in the years 622-1284 A. D. and 622-1433 A. D., respectively