## Why Non-Linearities Can Ruin The Heavy Tailed Modeler's Day (0)

Citations: | 16 - 8 self |

### BibTeX

@INPROCEEDINGS{Resnick_whynon-linearities,

author = {Sidney I. Resnick},

title = {Why Non-Linearities Can Ruin The Heavy Tailed Modeler's Day},

booktitle = {},

year = {},

publisher = {Birkhauser}

}

### OpenURL

### Abstract

. A heavy tailed time series that can be expressed as an infinite order moving average has the property that the sample autocorrelation function (acf) at lag h, converges in probability to a constant ae(h) despite the fact that the mathematical correlation typically does not exist. A simple bilinear model considered by Davis and Resnick (1996) has the property that the sample autocorrelation function at lag h converges in distribution to a non-degenerate random variable. Examination of various data sets exhibiting heavy tailed behavior reveals that the sample correlation function typically does not behave like a constant. Usually, the sample acf of the first half of the data set looks considerably different than the sample acf of the second half. A possible explanation for this acf behavior is the presence of nonlinear components in the underlying model and this seems to imply that infinite order moving average models and in particular ARMA models do not adequately capture dependency s...