A class of dynamic stochastic nonlinear models for hourly electricity price time series, where spikes and antispikes are a fundamental aspect of price phenomenology, are presented. In electricity series, spikes and antispikes appear randomly but in seasonally well defined windows of time (for example, spikes appear only during daylight, never during night time, in coincidence with electricity demand crests, whereas antispikes appear only during demand troughs). In each series, many concurrent mean reversion mechanisms can be present. In the proposed models, spikes and antispikes are generated by a mechanism, called stochastic resonating spiking (SRS), that mixes noise, nonlinearity and an external periodic forcing. Spikes appear only in selected windows of time, in accordance with the modeled data, and mean reversion can be complex. A phase space analysis will show that the SRS mechanism is based on the presence of a Hopf critical point for the dynamics. A quasilinear member of this class that supports SRS will be shown to be a second order Self-Excited Threshold AutoRegressive eXternally driven SETAR(2)X model, operated in an uncommon range of parameters. Econometric estimation of this SETAR(2)X model on electricity data will be shown to be simple, as far as only spikes are considered. When antispikes are included, polynomial extensions of the threshold model will be shown to be easier to estimate. The presented class is rather general, can include even more phenomenology features, and can be also used to model other seasonal commodity series.
Nonlinear dynamic models for spikes in electricity prices
Lucheroni, Carlo
2011-01-01
Abstract
A class of dynamic stochastic nonlinear models for hourly electricity price time series, where spikes and antispikes are a fundamental aspect of price phenomenology, are presented. In electricity series, spikes and antispikes appear randomly but in seasonally well defined windows of time (for example, spikes appear only during daylight, never during night time, in coincidence with electricity demand crests, whereas antispikes appear only during demand troughs). In each series, many concurrent mean reversion mechanisms can be present. In the proposed models, spikes and antispikes are generated by a mechanism, called stochastic resonating spiking (SRS), that mixes noise, nonlinearity and an external periodic forcing. Spikes appear only in selected windows of time, in accordance with the modeled data, and mean reversion can be complex. A phase space analysis will show that the SRS mechanism is based on the presence of a Hopf critical point for the dynamics. A quasilinear member of this class that supports SRS will be shown to be a second order Self-Excited Threshold AutoRegressive eXternally driven SETAR(2)X model, operated in an uncommon range of parameters. Econometric estimation of this SETAR(2)X model on electricity data will be shown to be simple, as far as only spikes are considered. When antispikes are included, polynomial extensions of the threshold model will be shown to be easier to estimate. The presented class is rather general, can include even more phenomenology features, and can be also used to model other seasonal commodity series.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
