48,659 research outputs found
Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form
A new state space approach is proposed to model the time- dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit a very accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence for time-dependence among the observed minimum returns.Extreme values, Generalized extreme value distribution, Markov chain Monte Carlo, Mixture sampler, State space model, Stock returns
A spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting
Renewable sources of energy such as wind power have become a sustainable
alternative to fossil fuel-based energy. However, the uncertainty and
fluctuation of the wind speed derived from its intermittent nature bring a
great threat to the wind power production stability, and to the wind turbines
themselves. Lately, much work has been done on developing models to forecast
average wind speed values, yet surprisingly little has focused on proposing
models to accurately forecast extreme wind speeds, which can damage the
turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto
model to forecast extreme and non-extreme wind speeds simultaneously. Our model
belongs to the class of latent Gaussian models, for which inference is
conveniently performed based on the integrated nested Laplace approximation
method. Considering a flexible additive regression structure, we propose two
models for the latent linear predictor to capture the spatio-temporal dynamics
of wind speeds. Our models are fast to fit and can describe both the bulk and
the tail of the wind speed distribution while producing short-term extreme and
non-extreme wind speed probabilistic forecasts.Comment: 25 page
Statistical Modeling of Spatial Extremes
The areal modeling of the extremes of a natural process such as rainfall or
temperature is important in environmental statistics; for example,
understanding extreme areal rainfall is crucial in flood protection. This
article reviews recent progress in the statistical modeling of spatial
extremes, starting with sketches of the necessary elements of extreme value
statistics and geostatistics. The main types of statistical models thus far
proposed, based on latent variables, on copulas and on spatial max-stable
processes, are described and then are compared by application to a data set on
rainfall in Switzerland. Whereas latent variable modeling allows a better fit
to marginal distributions, it fits the joint distributions of extremes poorly,
so appropriately-chosen copula or max-stable models seem essential for
successful spatial modeling of extremes.Comment: Published in at http://dx.doi.org/10.1214/11-STS376 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
"Bayesian Estimation and Particle Filter for Max-Stable Processes"
Extreme values are often correlated over time, for example, in a financial time series, and these values carry various risks. Max-stable processes such as maxima of moving maxima (M3) processes have been recently considered in the literature to describe timedependent dynamics, which have been difficult to estimate. This paper first proposes a feasible and efficient Bayesian estimation method for nonlinear and non-Gaussian state space models based on these processes and describes a Markov chain Monte Carlo algorithm where the sampling efficiency is improved by the normal mixture sampler. Furthermore, a unique particle filter that adapts to extreme observations is proposed and shown to be highly accurate in comparison with other well-known filters. Our proposed algorithms were applied to daily minima of high-frequency stock return data, and a model comparison was conducted using marginal likelihoods to investigate the time-dependent dynamics in extreme stock returns for financial risk management.
L_2 Differentiability of Generalized Linear Models
We derive conditions for differentiability of generalized linear models
with error distributions not necessarily belonging to exponential families,
covering both cases of stochastic and deterministic regressors. These
conditions induce smoothness and integrability conditions for corresponding
GLM-based time series models.Comment: 10 page
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