Abstract
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram.
| Original language | English |
|---|---|
| Pages (from-to) | 803-845 |
| Number of pages | 43 |
| Journal | Bernoulli |
| Volume | 20 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - May 2014 |
| Externally published | Yes |
Keywords
- ARMA
- Asymptotic theory
- Extremogram
- GARCH
- Multivariatiate regular variation
- Periodogram
- Spectral density
- Stationary sequence
- Stochastic volatility process
- Strong mixing