چکیده:
this paper proposes a new unit root test against the alternative of symmetric or asymmetric exponential smooth transition autoregressive (AESTAR) nonlinearity that accounts for multiple smooth breaks. We provide small sample properties which indicate the test statistics have good empirical size and power. Also, we compared small sample properties of the test statistics with Christopoulos and Leon-Ledesma (2010) test. The results indicate that our unit root test approach is superior to the test method of Christopoulos and Leon-Ledesma (2010) for both transition parameters (i.e. slow and fast speed), and the test power increases along with the frequency. We apply our test statistics for examining the real interest rate parity hypothesis among OECD countries.
خلاصه ماشینی:
Unit Root Test and AESTAR Nonlinearity with Multiple Smooth Breaks</H4> Suppose that a series {y }T follows the data generating process (DGP) as t t 1 yt (t) t , (1) where (t) Zt n k 1 1,k sin( 2kt ) T n k 1 2,k cos( 2kt ), T (t) is a time-varying deterministic component.
In order to obtain a global approximation from the smooth transition and unknown number, and to equip deterministic components with breaks, we follow Gallant (1981) approach with employing the Fourier n approximation and putting both terms of k sin( k 1 2kt T ) and n k cos( k 1 2kt T ) into the model.
We therefore calculate the critical values with the unit root test of Christopoulos and Leon-Ledesma (2010) for both models, in which one equipped only with intercept, and another contains both intercept and trend terms.
(b) When the degree of asymmetry is large, our unit root test is becoming more powerful (almost 20% and 32%, respectively) than the model with both intercept and trend in Christopoulos and Leon- Ledesma (2010).
In next step, we test the unit root hypothesis aiming at the RID series with our test statistic when multiple smooth breaks are allowed in intercept model.
Conclusion</H4> In this paper, we generalize the Sollis (2009) AESTAR nonlinear unit root test with allowing multiple smooth temporary breaks by calculating means in Fourier function.