Since Haslett and Raftery's paper Space-Time Modelling with Long-Memory Dependence: Assessing Ireland's Wind Power Resource (1989), modelling meteorological time series with long memory processes, in particular the ARFIMA model has become very common. Haslett and Raftery fitted an ARFIMA model on Irish daily wind speeds. In this paper, we try to reproduce Haslett and Raftery's results (focusing on the dynamic of the wind process, and not on cross-correlation and space dependencies), and show that an ARFIMA model does not properly capture the behaviour of the series (in Modelling daily windspeed in Ireland section). Indeed, the series show a periodic behaviour, that is not taken into account by the ARF-IMA model. Removing this periodic behaviour yields no results either, we therefore try to fit a GARMA model that takes into account both seasonality and long memory (in Seasonality and long memory using GAR-MA models section). If a GARMA process can be fitted to the data to model Irish daily data, we will show that these models could also be used to model Dutch hourly data.
SUMMARYWhen working on river floods-annual river levels maxima-, two approaches are usually considered: one inspired from Emil Gumbel where annual maxima are supposed to be i.i.d. and distributed according to Gumbel's distribution, and one inspired from Edwin Hurst where annual maxima are strongly dependent, and exhibit long range memory. This paper tries to solve this apparent paradox by deriving a dynamic model inspired from financial models, which does not take into account annual maxima only but also threshold exceedances. It studies the implications of such a paradox in terms of return period-a notion valid as long as the data are i.i.d-and of extremal events.
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