1st Workshop Industry and Price Forecasting - WIPFOR, Paris (France). 03-04 June 2010
Summary:
With worldwide liberalization of electricity markets, day-ahead price forecasting has become a crucial task in the operation activity of market agents to optimize their bidding strategies. Since market clearing prices are obtained by crossing stepwise supply and demand curves constructed from aggregated bids of buyers and sellers, electricity prices in day-ahead market are generally erratic and ill-behaved. In this context, electricity market agents assume a more intense risk exposure than in the traditional framework, and because of this, it is especially relevant not only to deal with point forecasts but also with complete probability density function forecasts.
Time series models constitute one of the most important approaches for short-term electricity price forecasting. Some initial contributions are the papers by [1] and [2] that pointed out that ARIMA (Auto Regressive Integrated Moving Average), dynamic regression and transfer function models are very accurate methods for prediction of the Spanish and Californian electricity prices. These conclusions are corroborated and extended to others electricity markets in [3], [4], [5], [6]. The success of these models lays in a well-established identification and diagnostic checking methodology (see [7] and [8]) that has been widely tested in many areas. They are able to deal with an important feature of electricity prices: the daily and hourly cycles. However, the stylized facts of electricity spot prices have been widely reported in the literature [9], [10], and they include some relevant features that are not properly captured by these models: different intra-day and intra-week patterns, time-varying volatility, fat-tailed and skewed distributions, extreme values and spikes. Different intra-week and intra-day patterns have been modeled by allowing parameters to switch over time through periodic models [11] or VARX models (Vector autoregressive with exogenous variables) [12]. TARX (Threshold Auto Regressive with exogenous variables) has been also used to model regime switching dynamics caused by explanatory variables [6]. Time-varying volatility has been tackled by including a GARCH (Generalized Auto Regressive Conditional Heteroskedasticity) disturbance term to the time series models [13]. Although they are not proved to increase point forecasting efficiency, they are interesting when volatility forecasts are required. The special underlying distribution of the electricity price stochastic process is one of its distinctive universal features. The empirical distributions obtained through the traditional Gaussian fitting framework rarely accomplish with the normality (or log-normality) assumption. Recent advances trying to find a satisfactory distribution include the work in [14], where a set of non-Gaussian distributions are tested on the price time series of different electricity markets. In [15], a set of semiparametric models whose density functions are estimated through kernel estimators are compared with their Gaussian counterparts. In [12], a VARX model specified through a sparse autoregressive coefficient matrix and skew t-distributed disturbance is proposed.
In this work, a novel seminonparametric regime switching model is proposed. The general structure corresponds to a regime switching transfer function model with ARCH disturbance, but two features are added: (1) the ability of the model to find hidden regime switching dynamics from explanatory variables and (2) nonparametric innovations.
Inspired in [16], the additional ability of finding hidden regime switching dynamics from explanatory variables is undertaken by modeling the conditional density function of each regime by means of a Radial Basis Function Network (RBFN), letting explanatory data speak from themselves without any previous assumption. Moreover, we do not assume a Gaussian distribution for the innovations inside each regime. Instead, we assume a seminonparametric (SNP) type of distribution suggested by Gallant and Tauchen [17] which uses Hermite expansions to approximate densities from a large class, including fat tails and skewed densities. This configuration leads us to a novel regime switching model where each inner model (or expert model) is associated to a hidden regime and specified by a SNP transfer function with ARCH disturbance whose parameters are fixed. The Radial Basis Function Network is in charge of computing the conditional probability of each regime at time t from the explanatory variables, in order to obtain the overall forecasted output by averaging the outputs of the expert models.
The forecasting ability of the proposed model is empirically tested with Spanish electricity price time series. The benefits of including switching regime dynamics and nonparametric innovations to forecast the complete density function of spot prices is investigated
Publication date: 2010-06-03.
Citation:
A. Cruz, A. Muñoz, Density forecasting of electricity spot prices with seminonparametric regime switching models, 1st Workshop Industry and Price Forecasting - WIPFOR, Paris (France). 03-04 June 2010.
