163,936 research outputs found
Joint Modelling of Gas and Electricity spot prices
The recent liberalization of the electricity and gas markets has resulted in
the growth of energy exchanges and modelling problems. In this paper, we
modelize jointly gas and electricity spot prices using a mean-reverting model
which fits the correlations structures for the two commodities. The dynamics
are based on Ornstein processes with parameterized diffusion coefficients.
Moreover, using the empirical distributions of the spot prices, we derive a
class of such parameterized diffusions which captures the most salient
statistical properties: stationarity, spikes and heavy-tailed distributions.
The associated calibration procedure is based on standard and efficient
statistical tools. We calibrate the model on French market for electricity and
on UK market for gas, and then simulate some trajectories which reproduce well
the observed prices behavior. Finally, we illustrate the importance of the
correlation structure and of the presence of spikes by measuring the risk on a
power plant portfolio
Volatility forecasting
Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1
Efficient Estimation of Mutual Information for Strongly Dependent Variables
We demonstrate that a popular class of nonparametric mutual information (MI)
estimators based on k-nearest-neighbor graphs requires number of samples that
scales exponentially with the true MI. Consequently, accurate estimation of MI
between two strongly dependent variables is possible only for prohibitively
large sample size. This important yet overlooked shortcoming of the existing
estimators is due to their implicit reliance on local uniformity of the
underlying joint distribution. We introduce a new estimator that is robust to
local non-uniformity, works well with limited data, and is able to capture
relationship strengths over many orders of magnitude. We demonstrate the
superior performance of the proposed estimator on both synthetic and real-world
data.Comment: 13 pages, to appear in International Conference on Artificial
Intelligence and Statistics (AISTATS) 201
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