# A Latent-Factor System Model for Real-Time Electricity Prices in Texas
## 2 Data and Variables
### Sample Period and Variables  
The sample period starts on 1 January 2015 and ends on 31 December 2018. Thus, we have a very large dataset since all the eight price series will appear together as endogenous variables in the multivariate response matrix. As noted earlier, we discuss at length the results for the following three zones: Houston, Austin, and the West. Additionally, we examine the merit-order effects stemming from three hours in a 24-h cycle: 4:00 a.m., 12:00 p.m. and, 4:00 p.m. The first is off-peak and the other two correspond to peak hours. There is nothing special about the specific hours we chose to work with; a similar analysis with other hours yields the same overall conclusions reported here. Table 1 provides the summary statistics for the prices ($/MWH) for the three hours and the three zones, respectively. The corresponding time-series plots of the nine series, shown in red, appear in Figure 2. In the analysis, however, we work with the natural log of the price data. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Mean** & **S.D.** & **Min** & **Max** \\ \hline  & \multicolumn{3}{c}{Houston} \\
4:00 a.m. & 16.40 & 5.83 & \(-\)14.83 & 75.66 \\
12:00 p.m. & 31.13 & 47.95 & 9.59 & 1110.26 \\
4:00 p.m. & 47.54 & 99.10 & 0.24 & 1348.34 \\  & \multicolumn{3}{c}{Austin} \\
4:00 a.m. & 16.14 & 6.31 & \(-\)14.89 & 97.65 \\
12:00 p.m. & 27.00 & 18.18 & 6.72 & 338.09 \\
4:00 p.m. & 42.38 & 85.96 & 0.11 & 1348.11 \\  & \multicolumn{3}{c}{West} \\
4:00 a.m. & 17.79 & 14.82 & \(-\)15.56 & 132.71 \\
12:00 p.m. & 27.55 & 23.43 & \(-\)16.88 & 408.91 \\
4:00 p.m. & 43.23 & 88.60 & \(-\)15.67 & 1384.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary statistics of the hourly prices ($/MWH) for Houston, Austin, and the West.  
Figure 1: The eight ERCOT zones (Source: www.ercot.com, accessed on 18 July 2020).  
One of the insights we hope to gain is to see how the one-hour-ahead in-sample estimates of the latent factor time series track the price plots in Figure 2. If we can show that there is a strong correlation between the estimated latent factor series and the price  
Figure 2: Time-series plots of the actual prices (solid red line) and model predicted prices (dash grey line) in Houston, Austin, and the West for the hours 4:00 a.m., 12:00 p.m. and 4:00 p.m.  
series, then that bodes well for the estimation of merit-order effects from alternative energy and baseload generation. On the other hand, if there is a very weak relationship between latent factors and the price series, then exogenous factors should suffice in understanding the fluctuations in the price data.  
A brief discussion of each of the independent variables now follows. These variables were selected based on careful data exploration via summary plots/correlation tables, practical considerations of data size, modeling aims, and computational complexities. Additionally, price formation in the ERCOT market has been analyzed in a variety of antecedent studies using many of the same data sources and variables employed in this study [14; 15; 16].  
The exogenous variables used in this study are split into those that appear in the observation and latent factor equations, respectively; these equations are detailed in the next section.  
_Observation Equation Exogenous Variables._ Wind generation, nuclear generation, solar generation, the Henry Hub gas price, and a dummy variable for spikes in prices that exceed $500 MWH are the exogenous variables. ERCOT analysts have noted that industrial customers tend to significantly scale back when prices exceed USD 500. So, a binary dummy variable for extreme price spikes is used. The solar generation variable and the dummy variable do not appear in the 4:00 a.m. equations. We downloaded daily natural gas prices for Henry Hub from the DOE/EIA (See: [[http://www.eia.gov/dnav/ng/hist/rngwhhdd.htm](http://www.eia.gov/dnav/ng/hist/rngwhhdd.htm)]([http://www.eia.gov/dnav/ng/hist/rngwhhdd.htm](http://www.eia.gov/dnav/ng/hist/rngwhhdd.htm)). Last accessed 18 July 2020).