scholarly journals MODELLING OF INTRADAY PHOTOVOLTAIC POWER PRODUCTION

2021 ◽  
Vol 40 (2) ◽  
pp. 105-124
Author(s):  
Noor ‘Adilah Ibrahim
Keyword(s):  
Gaussian Distribution ◽  
Heavy Tails ◽  
Deterministic Model ◽  
Autoregressive Process ◽  
Time Interval ◽  
Inverse Gaussian ◽  
Normal Inverse Gaussian Distribution ◽  
System Operator ◽  
Random Components ◽  
Normal Inverse Gaussian

Photovoltaic (PV) productions should occur within a time interval of sunlight. Time mismatches are detected between sunrise and first production hour as well as sunset and last production hour in a transmission system operator, Amprion, Germany. Hence, in this paper, we investigate this effect using an additive function of two seasonalities and a stochastic process. Both seasonalities are based on the mimicked locations, corrected by a weighing scale, depending on the first and last production hours' coordinates. The result shows that the proposed deterministic model could capture the effect of sunrise and sunset. Also, the dynamics of random components are sufficiently explained by an autoregressive process of order two. Finally, the Normal Inverse Gaussian distribution is shown as the best distribution in explaining noise behaviour, particularly heavy tails in the production's residuals, compared to the Gaussian distribution.

scholarly journals Clustering with the multivariate normal inverse Gaussian distribution

2016 ◽  
Vol 93 ◽  
pp. 18-30 ◽  
Author(s):  
Adrian O’Hagan ◽  
Thomas Brendan Murphy ◽  
Isobel Claire Gormley ◽  
Paul D. McNicholas ◽  
Dimitris Karlis
Keyword(s):  
Gaussian Distribution ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Multivariate Normal ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

Pattern Search for Generalized Hyperbolic Distribution and Financial Risk Measure

2012 ◽  
Vol 155-156 ◽  
pp. 424-429
Author(s):  
Xiu Fang Chen ◽  
Gao Bo Chen
Keyword(s):  
At Risk ◽  
Gaussian Distribution ◽  
Risk Measure ◽  
Inverse Gaussian Distribution ◽  
Pattern Search ◽  
Inverse Gaussian ◽  
Generalized Hyperbolic Distribution ◽  
Hyperbolic Distribution ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

A new parameter estimation--- pattern search algorithm based on maximum likelihood estimation is used to estimate the parameters of generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distribution, which are used to fit the log-return of Shanghai composite index. The goodness of fit is tested based on Anderson & Darling distance and FOF distance who pay more attention to tail distances of some distribution. Monte Carlo simulation are used to determin the critical values of Anderson & Darling distance and FOF distance of different distributions.Value at risk (VaR) and conditional value at risk (CVaR) are estimated for the fitted generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distributio.The results show that generalized hyperbolic distribution family is more suitable for risk measure such as VaR and CVaR than normal distribution.

scholarly journals THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS

2004 ◽  
Vol 07 (02) ◽  
pp. 177-192 ◽  
Author(s):  
FRED ESPEN BENTH ◽  
JŪRATĖ ŠALTYTĖ-BENTH
Keyword(s):  
Brownian Motion ◽  
Gaussian Distribution ◽  
Market Price ◽  
Energy Markets ◽  
Inverse Gaussian Distribution ◽  
Spot Price ◽  
Inverse Gaussian ◽  
Statistical Point ◽  
Normal Inverse Gaussian Distribution ◽  
Normal Inverse Gaussian

We model spot prices in energy markets with exponential non-Gaussian Ornstein–Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as the driving noise rather than Brownian motion. Instead of modelling the spot price dynamics as the solution of a stochastic differential equation with jumps, it is advantageous from a statistical point of view to model the price process directly. Imposing the normal inverse Gaussian distribution as the statistical model for the Lévy increments, we obtain a superior fit compared to the Gaussian model when applied to spot price data from the oil and gas markets. We also discuss the problem of pricing forwards and options and outline how to find the market price of risk in an incomplete market.

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