Statistical Modelling under the Non Stationary assumptions#
We now explore two approaches to statistical modelling for time series that exhibit trends or patterns.
In the first approach, i.e., detrending approach, we separate the deterministic and stochastic components and develop a statistical model only for the stochastic component. In the second approach, i.e., integrated approach, the deterministic component is incorporated directly into the statistical model. We apply the latter approach to extreme value analysis and review examples from the scientific literature.
Coles, Stuart, et al. An introduction to statistical modeling of extreme values. Vol. 208. London: Springer, 2001.
Katz, Richard W., Marc B. Parlange, and Philippe Naveau. “Statistics of extremes in hydrology.” Advances in water resources 25.8-12 (2002): 1287-1304.
Katz, Richard W. “Statistical methods for nonstationary extremes.” Extremes in a changing climate: Detection, analysis and uncertainty. Dordrecht: Springer Netherlands, 2012. 15-37.
Ragno, Elisa, et al. “A generalized framework for process-informed nonstationary extreme value analysis.” Advances in Water Resources 130 (2019): 270-282.