scholarly journals Residuals and goodness-of-fit tests for stationary marked Gibbs point processes

2012 ◽  
Vol 75 (2) ◽  
pp. 247-276 ◽  
Author(s):  
Jean-François Coeurjolly ◽  
Frédéric Lavancier
Keyword(s):  
Goodness Of Fit ◽  
Point Processes ◽  
Goodness Of Fit Tests ◽  
Gibbs Point Processes

scholarly journals Modeling Market Order Arrivals on the German Intraday Electricity Market with the Hawkes Process

2021 ◽  
Vol 14 (4) ◽  
pp. 161
Author(s):  
Nikolaus Graf von Luckner ◽  
Rüdiger Kiesel
Keyword(s):  
Electricity Market ◽  
Goodness Of Fit ◽  
Point Processes ◽  
Branching Ratio ◽  
Information Criterion ◽  
Order Type ◽  
Hawkes Process ◽  
Market Order ◽  
Jump Size ◽  
Goodness Of Fit Tests

We use point processes to analyze market order arrivals on the intraday market for hourly electricity deliveries in Germany in the second quarter of 2015. As we distinguish between buys and sells, we work in a multivariate setting. We model the arrivals with a Hawkes process whose baseline intensity comprises either only an exponentially increasing component or a constant in addition to the exponentially increasing component, and whose excitation decays exponentially. Our goodness-of-fit tests indicate that the models where the intensity of each market order type is excited at least by events of the same type are the most promising ones. Based on the Akaike information criterion, the model without a constant in the baseline intensity and only self-excitation is selected in almost 50% of the cases on both market sides. The typical jump size of intensities in case of the arrival of a market order of the same type is quite large, yet rather short lived. Diurnal patterns in the parameters of the baseline intensity and the branching ratio of self-excitation are observable. Contemporaneous relationships between different parameters such as the jump size and decay rate of self and cross-excitation are found.

scholarly journals Dependence Modeling in Energy Markets using Sibuya-type Copulas

2017 ◽  
Vol 6 (3) ◽  
pp. 43
Author(s):  
Nikolai Kolev ◽  
Jayme Pinto
Keyword(s):  
Goodness Of Fit ◽  
Basic Assumption ◽  
Energy Markets ◽  
Dependence Structure ◽  
Dependence Function ◽  
Dependence Modeling ◽  
Goodness Of Fit Tests ◽  
Oil And Natural Gas ◽  
Error Terms ◽  
Time Invariant

The dependence structure between 756 prices for futures on crude oil and natural gas traded on NYMEX is analyzed  using  a combination of novel time-series and copula tools.  We model the log-returns on each commodity individually by Generalized Autoregressive Score models and account for dependence between them by fitting various copulas to corresponding  error terms. Our basic assumption is that the dependence structure may vary over time, but the ratio between the joint distribution of error terms and the product of marginal distributions (e.g., Sibuya's dependence function) remains the same, being time-invariant.  By performing conventional goodness-of-fit tests, we select the best copula, being member of the currently  introduced class of  Sibuya-type copulas.

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