Least Absolute Deviation Estimation For AR(1)Process With A Nearly Unit Root

In this paper,we consider a first-order autoregressive process yt=ρnyt-1+ut.Using the method of Davis,Knight&Liu(Stochastic Processes and their Applications,1992),we can derive the Least Absolute Deviation(LAD)estimation and the asymptotic theory of parameter.First,we discuss the initial conditions of nearly unit root process.We derive that the asymptotic distribute of LAD estimation is Cauchy in nearly unit root stationarity case,and the asymptotic theory of LAD estimation,in explosiveness case,is also Cauchy,because the initial condition dominate the asymptotic.Then,when the model with y0=op(1)or 0 in nearly unit root process,we study the asymptotic theory of LAD estimation,and give its stochastic integral under some conditions.