The package tsExtremes includes functions for studying extreme features of heavy-tailed time series. It can be used to compute estimates of the tail index, the extremal index or cluster lengths of the series. These are statistics of the series summarizing the magnitude of extreme records, and the number of concomitant records.
Installation
To get started, install the package from Github using the command:
devtools::install_github('GBuritica/tsExtremes')R Package tutorial
This package tutorial includes two main windows on:
- Tail index inference
- In this vignette you will learn how to compute estimates of the tail index α of the series. The implementation is based on the Hill-type estimators in (Haan, Mercadier, and Zhou 2016).
- Cluster inference
- In this vignette you will learn how to implement block estimates of cluster statistics; see (Buriticá, Mikosch, and Wintenberger 2022). We consider the example of the extremal index based on the estimator proposed in (Buriticá et al. 2021), and also an example of cluster lengths (Buriticá and Wintenberger 2024).
References
Buriticá, G., N. Meyer, T. Mikosch, and O. Wintenberger. 2021. “Some Variations on the Extremal Index.” Zap. Nauchn. Semin. POMI. 30: 52–77.
Buriticá, G., T. Mikosch, and O. Wintenberger. 2022. “Large Deviations of Lp Blocks of Regularly Varyinig Time Series.” Stochastic Processes and Their Applications. 161: 68–101.
Buriticá, G., and O. Wintenberger. 2024. “On the Asymptotics of Extremal Lp-Blocks Cluster Inference.” arXiv:2212.13521.
Haan, L. de, G. Mercadier, and C. Zhou. 2016. “Adapting Extreme Value Statistics to Financial Time Series: Dealing Wih Bias and Serial Dependence.” Finance and Stochastics 20: 321–54.