Study on Linearity Test and Unit Root Testagainst Smooth Transition Autoregressive Model

Abstract: Considering the problem of carrying out linearity test and unit roottest against STAR model in two separate models, we believe that the two testsshould be carried out in a single STAR model, first the unit root test and thenthe linearity test. The corresponding distributions and critical values oft-statistic and F-statistic are also provided in this paper. The result shows thatthe distributions of the two statistics are non-standard, and larger than thecritical values of DF test t-statistic and standard F-statistic respectively withthe same probability. Besides, it is testified by the Monte Carlo experiment that the efficiency of t-statistic proposed inthis paper is significantly higher than that of DF unit root test statistic.Only when the non-stationarity characteristic of the series is verysignificant, can DF test detects the unit roots in it. Therefore, it isnecessary to conduct a unit root test in a nonlinear model.