On a transform for modeling skewness

Li, Kang; Damien, Paul; Walker, Stephen G.

doi:10.1214/20-bjps477

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…But, for this assumption to hold, the data distribution has to be examined carefully; see Refs. [24,25]. The assumption of normality for the error distribution might be justified if the third and fourth moments-skewness and kurtosis-of the data distribution were approximately symmetric and exhibited low kurtosis.…”

Section: Regression Analysis Of Price (Usd/mwh) Data For West North A...mentioning

confidence: 99%

The Impact of Renewable Energy Tax Incentives on Electricity Pricing in Texas

Rudolph

Damien

2023

Applied Sciences

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Texas has abundant natural resources, making it a good place for renewable energy facilities to build. Unfortunately, property taxes are the highest tax on an incoming renewable energy facility in the state. In order to increase renewable energy in the state, Texas tax code Chapter 313 was introduced. Chapter 313 allows school districts the opportunity to offer a 10-year limit, ranging from USD 10 million to USD 100 million, on the taxable value of a new green energy project. With Chapter 313 ending in 2022, the following question is raised: how do tax incentives that increase the number of applications for producing renewable energy in Texas impact the wholesale, real-time pricing of electricity in the state? Skew-t regression models were implemented on a large dataset, focusing on the designated North, Houston, and West regions of the Electricity Reliability Council of Texas (ERCOT), since these regions account for 80% of the state’s energy consumption. Analysis focused on the hours ending at 3 AM, 11 AM, and 4 PM, due to the ERCOT’s time-of-day pricing. Three key findings related to the above question resulted. First, tax incentives that increase the number of active wind and solar facilities lead to a statistically significant (p < 0.0001) reduction in wholesale electricity price (USD/MWh), ranging between 2.31% and 6.6% across the ERCOT during different hours of the day. Second, for a 10% increase in tax-incentivized green energy generation, during a 24-hour period, there is a statistically significant (p < 0.0001) reduction in the generation cost (USD/MWh), ranging between 0.82% and 1.96%. Finally, electricity price reductions from solar energy are much lower than those from wind generation and/or are not statistically significant.

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Section: Regression Analysis Of Price (Usd/mwh) Data For West North A...mentioning

confidence: 99%

The Impact of Renewable Energy Tax Incentives on Electricity Pricing in Texas

Rudolph

Damien

2023

Applied Sciences

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“…The GMU was introduced by Kang et al (2020), based on a simple skew transformation that allows one to model varying levels of skewness and tail behaviors. Denoting the four-parameter family of GMU densities as Y ∼ GMU(µ, α, β, λ), where µ, α, β and λ are the location, kurtosis, scale and skewness parameters, respectively, then, a member from this family has probability density function f (y) given by:…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, they show that the GMU includes, among others, the Laplace and the normal distributions as special cases. While Kang et al (2020) showed that the GMU density outperforms several alternatives, including the skewed-t, skewed-normal, asymmetric Laplace, etc., that research did not address how, in a time series context, the conditional moments of the GMU density could be estimated dynamically as functions of several exogenous factors. The extension to a multi-factor GMU is one of the main theoretical contributions in this paper, as well as demonstrating its applied benefits in the electricity price context.…”

Section: Introductionmentioning

confidence: 99%

Bayesian estimation of electricity price risk with a multi-factor mixture of densities

Walker

Damien

et al. 2022

Quantitative Finance

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The risks in daily electricity prices are becoming substantial and it is clear that improvements in price density forecasting can translate into improved improved risk management. However, the specification of the most appropriate price density function is challenging as the best functional forms differ by time of day evolve over time, dynamically respond to fluctuating exogenous factors such as wind speed and solar irradiance. This research develops and tests a new flexible functional form based upon the Gamma Mixture of Uniform (GMU) densities which effectively avoids the choice of a particular density function and has conditional moments specified as a function of the dynamic exogenous drivers. Empirical testing shows that it outperforms the multifactor skewed student-t family of densities, previously advocated in this context. Additionally, using Bayesian estimation the new methodology provides a complete description of the uncertainty in the estimation of the coefficients for those exogenous factors. Empirical testing on dayahead hourly electricity prices in the German market from 2012 to 2016, where renewable energy sources, such as wind and solar, play a critical role in the formation of electricity price risk, validates the extra accuracy of this formulation.

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