Abstract: The statistical modelling of precipitation data for a
given portion of territory is fundamental for the monitoring of
climatic conditions and for Hydrogeological Management Plans
(HMP). This modelling is rendered particularly complex by the
changes taking place in the frequency and intensity of precipitation,
presumably to be attributed to the global climate change. This paper
applies the Wakeby distribution (with 5 parameters) as a theoretical
reference model. The number and the quality of the parameters
indicate that this distribution may be the appropriate choice for
the interpolations of the hydrological variables and, moreover, the
Wakeby is particularly suitable for describing phenomena producing
heavy tails. The proposed estimation methods for determining the
value of the Wakeby parameters are the same as those used for
density functions with heavy tails. The commonly used procedure
is the classic method of moments weighed with probabilities
(probability weighted moments, PWM) although this has often shown
difficulty of convergence, or rather, convergence to a configuration
of inappropriate parameters. In this paper, we analyze the problem of
the likelihood estimation of a random variable expressed through its
quantile function. The method of maximum likelihood, in this case,
is more demanding than in the situations of more usual estimation.
The reasons for this lie, in the sampling and asymptotic properties of
the estimators of maximum likelihood which improve the estimates
obtained with indications of their variability and, therefore, their
accuracy and reliability. These features are highly appreciated in
contexts where poor decisions, attributable to an inefficient or
incomplete information base, can cause serious damages.
Abstract: Electricity markets throughout the world have
undergone substantial changes. Accurate, reliable, clear and
comprehensible modeling and forecasting of different variables
(loads and prices in the first instance) have achieved increasing
importance. In this paper, we describe the actual state of the
art focusing on reg-SARMA methods, which have proven to be
flexible enough to accommodate the electricity price/load behavior
satisfactory. More specifically, we will discuss: 1) The dichotomy
between point and interval forecasts; 2) The difficult choice between
stochastic (e.g. climatic variation) and non-deterministic predictors
(e.g. calendar variables); 3) The confrontation between modelling
a single aggregate time series or creating separated and potentially
different models of sub-series. The noteworthy point that we would
like to make it emerge is that prices and loads require different
approaches that appear irreconcilable even though must be made
reconcilable for the interests and activities of energy companies.