Abstract
We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of long strange intervals turns out to change dramatically once the exponent of regular variation of the coefficients becomes smaller than 1, and then the rate of growth is determined both by the exponent of regular variation of the coefficients and by the heaviness of the tail distribution of the noise variables.
Original language | English |
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Pages (from-to) | 119-148 |
Number of pages | 30 |
Journal | Stochastic Processes and their Applications |
Volume | 93 |
Issue number | 1 |
DOIs | |
State | Published - May 2001 |
Keywords
- 60F15
- Applications in finance
- Extreme value distribution
- Heavy tails
- Insurance
- Large deviations
- Long-range dependence
- Moving average process
- Primary 60G10
- Regular variation
- Secondary 60G70
- Telecommunications