## 2 Data Details
### Dependent Variable: Price (USD/MWh)  
We selected three hours in a 24 h cycle, as these are a fair representation of electricity usage and pricing. The hours we chose end at 3 AM, 11 AM, and 4 PM. Demand and price volatility tend to be the highest between 4 and 6 PM. The early morning hours have the least variability, and solar generation is absent after sunset. The 11 AM hour is more like the 4 PM hour, but not as variable.  
Consider the summary statistics for the price variables in Table 2. Panels A through C of the table provide the price (USD/MWh) summaries for the hours ending at 3 AM, 11 AM, and 4 PM for North, Houston, and West regions, respectively. North and Houston are the largest energy-using zones in Texas. The West zone has the most wind-generating capacity. The mean and median prices in the three regions are generally comparable for the three hours. The volatility, as depicted by the standard deviation, is largest in West Texas, since this region depends primarily on wind generation. Other key differences are the skewness and kurtosis values across the zones for the three hours.  
These features of the price data are likely the result of differing energy demand levels across the three regions. It is important to understand the impact on prices resulting from large fluctuations in demand during peak and off-peak hours, even though it is difficult to pinpoint the exact reasons for some of these variations; seasonality plays a role. But another unique electricity pricing feature in the ERCOT must be considered in any statistical analysis of pricing data: wholesale price per MWh can be negative or close to zero, due to Locational Marginal Pricing (LMP).  
LMP is a mechanism by which wholesale electricity prices quantify the value of electric power in different regions in the ERCOT, taking into consideration factors such as demand, generation, and the supply constraints inherent in the ERCOT's state-wide transmission system. Theoretically and practically, LMP values can be negative. This happens when there is a surplus in generation. In such instances, certain resources--typically wind--are forced to curtail production. To remain economically viable, wind-generating plants are given a Production Tax Credit, which is paid in USD/MWh. In these instances, the real-time wholesale price of electricity will be negative, or almost zero.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline Hour & Sample Size & Mean & Minimum & Median & Maximum & SD & Skewness & Kurtosis \\
3:00 AM & 5844 & 15.452 & 0.010 & 16.930 & 82.700 & 6.188 & \(-\)0.078 & 9.452 \\
11:00 AM & 5844 & 24.703 & 0.070 & 21.740 & 556.920 & 17.688 & 14.780 & 317.502 \\
4:00 PM & 5844 & 42.747 & 0.550 & 24.980 & 2171.230 & 95.176 & 11.139 & 168.636 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary statistics for price (USD/MWh).  
For the above reasons, rather than using seasonal and/or LMP variables, we created dummy variables, based off the price data distributions shown in Table 2. These variables are critical to understanding how real-time prices are influenced by aberrant events or times within the dataset.  
We also do not include lagged dependent variables, since the focus is on estimation, not prediction, in our real-time pricing regression models. Autoregressive and moving average variables are generally beneficial in time series regressions used for predictive analysis [18]. Such variables, typically, tend to increase predictive accuracy, but they also tend to dampen the effect sizes of other factors in the model, including outlier events captured via dummy variables, such as the LMP in energy models [19]. [PERSON] et al. (2019) showed that autoregressive terms could prove useful in day-ahead ERCOT pricing models, where prices are set a day in advance of the supply of, and demand for, electricity the following day [20]. This is not the case in real-time pricing, where prices change every hour of the day, due to trading volatilities and other market-based demand and supply issues.