Pitfalls of Fitting Autoregressive Models for Heavy-Tailed Time Series

Springer Science and Business Media LLC - Tập 1 - Trang 391-422 - 1999
Paul D. Feigin1, Sidney I. Resnick2
1Faculty of Industrial Engineering and Management, Technion‐Israel Institute of Technology, Haifa, Israel
2School of Operations Research and Industrial Engineering, Cornell University, Ithaca, USA

Tóm tắt

We consider the analysis of time series data which require models with a heavy-tailed marginal distribution. A natural model to attempt to fit to time series data is an autoregression of order p, where p itself is often determined from the data. Several methods of parameter estimation for heavy tailed autoregressions have been considered, including Yule–Walker estimation, linear programming estimators, and periodogram based estimators. We investigate the statistical pitfalls of the first two methods when the models are mis-specified—either completely or due to the presence of outliers. We illustrate the results of our considerations on both simulated and real data sets. A warning is sounded against the assumption that autoregressions will be an applicable class of models for fitting heavy tailed data.

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