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Bayesian Estimation of AR (1) with Change Point under Asymmetric Loss Functions
並列摘要
The object of this paper is a Bayesian analysis of the autoregressive model X_t=β_1X_(t-1)+ε_t, t=1,..,m and X_t=β_2X_(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_2 are 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.
延伸閱讀
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