Bayesian Unit Root Test for AR(1) Model with Trend Approximated

  • Jitendra Kumar Central University of Rajasthan
  • Varun Varun Central University of Rajasthan
  • Dhirendra Kumar Central University of Rajasthan
  • Anoop Chaturvedi University of Allahabad
Keywords: AR model, Linear spline function, Unit root, Posterior odds ratio.


The objective of present study is to develop a time series model for handling the non-linear trend process using a spline function. Spline function is a piecewise polynomial segment concerning the time component. The main advantage of spline function is the approximation, non linear time trend, but linear time trend between the consecutive join points. A unit root hypothesis is projected to test the non stationarity due to presence of unit root in the proposed model. In the autoregressive model with linear trend, the time trend vanishes under the unit root case. However, when non-linear trend is present and approximated by the linear spline function, through the trend component is absent under the unit root case, but the intercept term makes a shift with r knots. For decision making under the Bayesian perspective, the posterior odds ratio is used for hypothesis testing problems. We have derived the posterior probability for the assumed hypotheses under appropriate prior information. A simulation study and an empirical application are presented to examine the performance of theoretical outcomes.

Author Biography

Jitendra Kumar, Central University of Rajasthan
Department of Statistics Central University of Rajasthan Bandersindri, District: Ajmer, Rajasthan, India-305817


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How to Cite
Kumar, J., Varun, V., Kumar, D., & Chaturvedi, A. (2020). Bayesian Unit Root Test for AR(1) Model with Trend Approximated. Statistics, Optimization & Information Computing, 8(2), 425-461.
Research Articles