Estimation Of The Auto-regression Moving Average Process With Heavy Tailed

We consider a causal, stationary, autoregressive, moving average [ARMA(p,q)] process with heavy tailed noise variables. We develop the definition of the inverse autocorrelation function, and obtain the G-Spectral estimator of the inverse autocorrelation function. We prove the weak consistency of the estimator, which is based on the point process convergence. Then by using the inverse autocorrelation function we get another means of moments parameter estimates on the MA part of ARMA(p,q), Cleveland-Parzen estimates.Moreover, in this paper we study the unstable autoregressive model for first order [AR(1)] with heavy tailed innovations. The consistency of the ordinary least squares estimator n is obtained for = -1, and the limiting distribution of n is established as a function of a Levy process. These results are useful in testing for the presence of unit roots when the innovations are heavy tailed.