A Robust Sieve Bootstrap Unit Root Test On The Initial DGP

Commonly used unit root tests of time series are given a proper initial value, however, shocks often make actual time series data difficult to meet the initial conditions of unit root test. And the generative process of historical time series data might affect the inference of the random variable stability, in the practical application this influence is often ignored. This paper argues that the sample time series data is a part of its random variable time series data. We can’t make a difference between the initial DGP and the sample DGP when infering the stability of random variable, but the two processes should be combined. First, regarding stationary or non-stationary historical process, we deduce the asymptotic distribution of DF statistics of unit root test, and discuss that the historical process how to influence the power and size of unit root tests. The research discovers that when the historical process is non-stationary, DF test with no drift items has the question of null hypothetical false rejection, and the longer term of the historical process, the power of DF test is smaller, namely the risk of false errors will be aggravated. When the historical process is stationary, it with longer term does not affect the inference of DF test. Second, based on the sieve bootstrap, we propose a sieve bootstrap test of unit root and consider its finite sample performance. Through Monte Carlo simulations, we investigate the finite sample distributions and give the critical value. The research discovers that when the historical process is non-stationary or stationary, the statistics of a sieve bootstrap unit root test don’t have serious size distortions. Finally, an example is presented to illustrate the sieve bootstrap test statistics for unit root tests.