THE ESTIMATION OF THE PARAMETERS OF AUTOREGRESSIVE PROCESS WITH DISTURBING NOISE AND ITS ASYMTOTIC PROPERTIES

In this paper, we disouss the estimation of autoregressive model with disturbing noise following Y（t）=X（t）+Z（t）, where X（t） is an AR（p）time series and Z（t） is an i. i. d. noise sequence. The paper gives the strong convergence rate of the estimators obtained and show that the estimtors are asymptotically normally distributed. A method of estimating order of the model is given and proven to be strongly consistent.