Abstract
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.
Highlights
The Box-Jenkins approach for analyzing and modelling time series emerged as one of the most acceptable field of data analytic in which anyone may integrate various information from the recorded data through a modelling or methodology approach
In a time series model, linear dependence occurs when series is nearly symmetric to a lagged version of itself, and disturbance coefficients are constant over time, i.e., series is stationary with its mean, variance and autocorrelation
We propose the Bayesian unit root test for testing the presence of unit root in an autoregressive model with a non-linear time trend
Summary
The Box-Jenkins approach for analyzing and modelling time series emerged as one of the most acceptable field of data analytic in which anyone may integrate various information from the recorded data through a modelling or methodology approach. [3] and [4] demonstrated that Bayesian unit root tests based on flat prior assumptions perform better than classical methods. [7] studied the unit root hypothesis for an autoregressive model with a polynomial trend under a Bayesian framework. To model the non-linear trend components, one may require a polynomial of high order in which estimates of coefficients are usually unstable. The main emphasis is to build up a Bayesian approach for testing the unit root in an autoregressive time series (AR) model with a non-linear time trend. We obtain the posterior odds ratio for the considered hypotheses of the model under the appropriate prior assumptions. Dataset on import series of Asian Regional Forum (ARF) countries are taken to demonstrate the applicability of linear spline function in the time series model
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