Common Unobserved Determinants of Intraday Electricity Prices.

• Author: Thomaidis, Nikolaos S.

1. INTRODUCTION AND LITERATURE REVIEW

   The deregulation of power systems and the introduction of competitive electricity market designs have led to tangible benefits for the consumers and the environmental considerations in most developed countries. The increased benefits however often come with major challenges to be faced by market regulators and participants, most prominent being the great deal of uncertainty surrounding the determination of electricity prices in the short and medium term. To achieve an accurate description of the power price dynamics in electricity markets, research contributions continue to explore and provide relevant advances in statistical modeling. Even with a stream of new modeling contributions in patterns and determinants of price setting, the very nature of the underlying commodity (electrical power) and the rules governing its trading in competitive markets continue to present implementation difficulties for vested policy makers.

   The modern approach to electricity price modelling is to treat hourly contracts as separate units in a panel and employ a multivariate econometric device (such as VARMAX models) to describe the dynamics of the entire cross section. This is advocated by the fact that trading in dayahead markets is discontinuous and the price of all hourly contracts is determined simultaneously using the same information available until the gate closure time (see e.g. Huisman et al., 2007). However, the allure of this approach introduced new methodological research questions. Extant empirical research on the stochastic properties of electricity price time-series revealed that, in practice, the confuence of exogenous factors along with long-memory and multiple levels of seasonality work together to form a complex data-generating process. In order to capture cross-sectional and intertemporal relationships between the prices of hourly power contracts, the model-builder is left to contemplate a complex model parametrization. But it is well known that such models are prone to numerical instability, over-ftting and poor out-of-sample forecasting performance.

   A natural approach to dealing with complexity and dimensionality issues is the imposition of a factor structure in the dynamics of the price curve. This is also dictated by the very nature of trading in electricity markets and the high levels of observed cross-dependence between the prices of contracts controlling power delivery in nearby hour zones of the following operating day or in bidding areas with physical connectivity. The literature of factor analytic approaches to power price modelling is thin compared to univariate or other multivariate time series models. (1) Wolak (2000) applies principal components analysis (PCA) to hourly and half-hourly price quotes of several national electricity markets (England, Wales, Norway, Sweden, Victoria and New Zealand). Vehvilainen and Pyykkonen (2005) apply a structural factor approach to the Elspot power market, with a view on explaining the statistical properties of day-ahead prices based on an array of fundamentals (temperature, precipitation, load, baseload power supply, etc.). Predictions about fundamentals are then used as a basis for generating forecasts about price series. Alonso et al. (2011) apply a dynamic factor model for long-term forecasting of Spanish electricity prices. They assume that the dynamics of the unobserved price components can be adequately described by a seasonal VARMAX model that considers not only dynamic cross-dependencies among unobserved components but also seasonal variations. The parameters of the model as well as the number of latent components are estimated using state-space techniques. Munoz et al. (2013) study the properties of the Iberian day-ahead electricity prices using principal components analysis. By ordering the eigenvalues of the sample correlation matrix, the authors conclude that only three factors can adequately explain the cross-section of power prices.

   In a European study, Liebl (2013) applies a dynamic semiparametric factor model to the prices of the day-ahead power delivery contracts traded in the European Electricity Exchange. His modelling framework assumes that factor loadings are parametric functions of the delivery hour and possibly other exogenous variables. These functions are then combined with univariate regime-switching models for the factor dynamics to generate estimates for individual hourly prices. Liebl (2013) finds a great deal of commonality in European electricity prices, as three factors capture almost 80% of the total data variance. Raviv et al. (2015) apply a variety of univariate, multivariate and dimensionality reduction techniques to the task of forecasting electricity prices in the NordPool market. They show that the accurate modelling of dynamic cross-sectional linkages between the values of hourly contracts leads to superior out of-sample performance, even if the purpose is to predict daily averaged day-ahead prices. Further improvements in predictive accuracy are observed by imposing a dynamic factor structure in the entire array of hourly contracts and by modelling the dynamic properties of the reduced-size array of the extracted factor time-series. Maciejowska and Weron (2015) focus on short- and medium-term forecasting of the value of different hourly power delivery contracts pertaining to several transmission zones of the Pennsylvania-New Jersey-Maryland (PJM) interconnection. They apply PCA to extract the common drivers of PJM hourly and regional electricity prices and compare the predictive ability of three dynamic factor models with restrictive vector autoregressions and univariate AR models. Their conclusion is similar to Raviv et al. (2015) as to the predictive value of the intraday or interzonal structure of power prices when it comes to generating forecasts for the day-ahead PJM market. The relative superiority of factor models does not significantly change with the forecasting horizon.

   A common critique to all factor modelling techniques presented above is the fact that although they manage to achieve dimensionality reduction by linking the co-variation of the price vector to a smaller number of common factors, the extracted systematic components often lack interpretation. Hence, it becomes very difficult for the analyst to understand the nature of the latent forces moving the panel of power prices and, in consequence, use them as indicators for generating price forecasts or for policy evaluation. This is particularly the case with panels admitting a block structure, i.e. panels where units represent different hours of power delivery, national markets or bidding zones. In this data environment, global factors, commonly influencing the entire cross-section, and block-specific latent components, influencing a group of variables representing a portion of the panel, work together to form a complex hierarchical factor structure (Han and Caner, 2017). In principle, the common factors extracted using PCA-based methods are a mixture of global and group-specific effects, with limited use for structural analysis. Multilevel or hierarchical factor models that perform an explicit separation of common effects between different blocks of panel units seem more advantageous in this respect.

   In a recent working paper that is related to our approach, Ergemen and Rodriguez-Caballero (2017) apply a two-level factor model to separate area-specific from global effects in the price formation mechanism of several bidding zones within the NordPool. This study takes into account another important feature of the day-ahead electricity prices (long memory) and employs the sequential least-squares (LS) approach of Breitung and Eickmeier (2016) to estimate the components of the factor model (global factor scores, regional systematic shocks, loadings, etc.). Contrary to other papers employing hierarchical or multilevel factor models in macroeconomic analysis and forecasting tasks, this study explicitly deals with the model selection issue in a multilevel factor setting. In particular, the authors employ a mixture of the Hallin and Liska (2007); Alessi et al. (2007)'s data-driven model selection criterion with set algebra techniques to determine the dimensions of the global and regional factor spaces. Small-sample properties of the proposed model selection procedure are investigated through simulation experiments.

   The approach used in this study is more in the spirit of Ergemen (2016); Ergemen and Rodriguez-Caballero (2017) and Breitung and Eickmeier (2016). We employ our methods in a richer dataset reflecting the power trading activity in the PJM interconnection. Our panel includes 192 variables in the cross-section (8 transmission zones times 24 hourly contracts per zone). To the best of our knowledge, there is no study up to now examining dynamic properties of PJM prices in a multilevel factor model setting. This presents us with additional opportunities. With our approach we are able to attribute the stochastic co-variation of power prices to pervasive and regional forces. Moreover, by explicitly separating deterministic from stochastic common factors, we can tell whether seasonality and other predictable features of power trading dominate market-wide unanticipated events.

   Our study also contributes to the literature on econometric model-building for energy markets. Most of the papers employing multilevel or hierarchical factor model settings do not consider model selection thoroughly. They typically fix the number of global factors or the dimension of lower-level common components (influencing only a block of variables in the panel) using heuristic criteria. However, this approach may often lead to a misinterpretation of global/regional features and poor understanding of the true sources of co-movement in panel variables (Han and Caner, 2017). This paper places equal emphasis on model selection. It is...