Bayesian analysis of a stationary AR(1) model and outlier

The time varying observation recorded in chronological order is called time series. The extreme values are from the same time series model or appear because of some unobservable causes having serious implications in the estimation and inference. This change deviate the error more and the recorded observation is called outlier. The present paper deals the Bayesian analysis to the extreme value(s) is/are from the same time series model or appears because of some unobservable causes. We derived the posterior odds ratio in different setups of unit root hypothesis. We have also explored the possibility of studying the impact of outlier on stationarity of time series. Using the simulation study, it has been observed that if outlier is ignored a non-stationary series concluded difference stationary.