Comparison of hidden and observed regime-switching autoregressive models for (<i>u</i>, <i>v</i>)-components of wind fields in the northeastern Atlantic

Abstract

Several multi-site stochastic generators of zonal and meridional components of wind are proposed in this paper. A regime-switching framework is introduced to account for the alternation of intensity and variability that is observed in wind conditions due to the existence of different weather types. This modeling blocks time series into periods in which the series is described by a single model. The regime-switching is modeled by a discrete variable that can be introduced as a latent (or hidden) variable or as an observed variable. In the latter case a clustering algorithm is used before fitting the model to extract the regime. Conditional on the regimes, the observed wind conditions are assumed to evolve as a linear Gaussian vector autoregressive (VAR) model. Various questions are explored, such as the modeling of the regime in a multi-site context, the extraction of relevant clusterings from extra variables or from the local wind data, and the link between weather types extracted from wind data and large-scale weather regimes derived from a descriptor of the atmospheric circulation. We also discuss the relative advantages of hidden and observed regime-switching models. For artificial stochastic generation of wind sequences, we show that the proposed models reproduce the average space-time motions of wind conditions, and we highlight the advantage of regime-switching models in reproducing the alternation of intensity and variability in wind conditions. ton, 2010; Ailliot et al., 2006;Wikle et al., 2001;Fuentes et al., 2005). Except in Hering et al. (2015), these models are designed for short-term wind prediction and not for the generation of artificial conditions of {u t , v t }. Consequently they are not focused on reproducing the same statistics we are interested in, namely, the marginal distribution of {u t , v t } and its spatiotemporal dynamics. In Hering et al. (2015), a stochastic generator for multiple temporal and spatial scalesPublished by Copernicus Publications.

A Non‐Gaussian Spatio‐Temporal Model for Daily Wind Speeds Based on a Multi‐Variate Skew‐t Distribution

“…Environmental data often exhibit departures from Gaussianity, such as skewness and heavy tails. Traditionally, to continue exploiting the appealing properties of the normal distribution and the well‐developed theory of Gaussian processes, a transformation is usually applied to the data; for example, a square root transformation (Gneiting, ), a power transformation (Ailliot et al ; Bessac et al ) or a Gaussian copula (Hering et al ). Only recently have there been studies that exploit the flexibility of skew‐elliptical distributions, of which the skew‐ t (Azzalini and Capitanio, ) and the skew‐normal (Azzalini, ) distributions are special cases that directly address the skewness and excess kurtosis that are commonly found in wind data.…”

“…2002), a power transformation (Ailliot et al, 2015b;Bessac et al, 2016) or a Gaussian copula . Only recently have there been studies that exploit the flexibility of skew-elliptical distributions, of which the skew-t (Azzalini and Capitanio, 2003) and the skew-normal (Azzalini, 2005) distributions are special cases that directly address the skewness and excess kurtosis that are commonly found in wind data.…”

Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature

“…It leads to a VAR model for dry days and an other VAR model for wet days (Richardson, 1981). The MSVAR model is more general since the regimes are not observed (see (Bessac et al, 2016) for a comparison of models with observed and latent regimes for wind data). (1) Rennes (2) Le Mans (3) Paris (4) Beauvais (5) Strasbourg (6) Vichy (7) Biarritz (8) Toulouse (9) Carcassone (10) Nimes (11) Mont−Aigoual (12) Figure 1: Considered stations.…”

“…This model is a mixture of three autoregressive models which accommodate "rising", "falling" and "normal" states in the runoff process. (Bessac et al, 2016) and proposed Markov Switching VAR models to exhibit wind regimes from multivariate meteorological time series. These models are common for econometric time series too (Hamilton, 1989) (Krolzig, 2013).…”

“…However, this approach often requires an important modelling effort. And, for some applications, it is really difficult to find convenient parametric models (Bessac et al, 2016). A typical difficulty, is that one needs to obtain a first (non parametric) fit of the model to be able to choose parametric shapes.…”