Bayesian Estimation of AR (1) with Change ...

The object of this paper is a Bayesian analysis of the autoregressive model X_t = β_1 X_(t-1)+ε_t ,t=1,..,m and X_t = β_2 X_(t-1)+ε_t ,t=m+1,..,n where 0 < β_1,β_2 < 1, and ε_t is independent random variable with an exponential distribution with mean θ_1 but later it was found that there was a change in the process at some point of time m which is reflected in the sequence after ε_(m )is changed in mean θ_2. The issue this study focused on is at what time and which point the change begins to occur. The estimators of m, β_1 〖,β〗_2 and θ_1,θ_2are derived from Asymmetric loss functions namely Linex loss & General Entropy loss functions. Both the non-informative and informative priors are considered. The effects of prior consideration on Bayes estimates of change point are also studied.