7,662 research outputs found
Asymptotic behaviour of estimators of the parameters of nearly unstable INAR(1) models
A sequence of first-order integer-valued autoregressive type (INAR(1))
processes is investigated, where the autoregressive type coefficients converge to 1. It
is shown that the limiting distribution of the joint conditional least squares estimators
for this coefficient and for the mean of the innovation is normal. Consequences
for sequences of Galton{Watson branching processes with unobservable immigration,
where the mean of the offspring distribution converges to 1 (which is the
critical value), are discussed
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
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