Pitfalls of Fitting Autoregressive Models for Heavy{tailed Time Series

We consider the analysis of time series data, with particular emphasis on series which have a heavy-tailed structure | that is, whose marginal distributions have a right tail which is regularly varying at innnity with index ?. A natural model to attempt to t to time series data is an autoregression of order p, where p itself is often determined from the data. Recently several methods of parameter estimation for heavy tailed series have been considered, including Yule-Walker estimation, linear programming estimators, and periodogram based estimators. We investigate the statistical pitfalls of the rst two methods when the models are mis-speciied | either completely or due to the presence of outliers. We illustrate the results of our considerations on both simulated and real data sets.