FORECASTING SPOT ELECTRICITY PRICES WITH TIME SERIES MODELS

In this paper we study simple time series models and assess their forecasting performance. In particular we calibrate ARMA and ARMAX (where the exogenous variable is the system load) processes. Models are tested on a time series of California power market system prices and loads from the period proceeding and including the market crash.Electricity, price forecasting, ARMA model, seasonal component

Heavy tails and electricity prices: Do time series models with non-Gaussian noise forecast better than their Gaussian counterparts?

This paper is a continuation of our earlier studies on short-term price forecasting of California electricity prices with time series models. Here we focus on whether models with heavy-tailed innovations perform better in terms of forecasting accuracy than their Gaussian counterparts. Consequently, we limit the range of analyzed models to autoregressive time series approaches that have been found to perform well for pre-crash California power market data. We expand them by allowing for heavy-tailed innovations in the form of α-stable or generalized hyperbolic noise.Electricity; price forecasting; heavy tails; time series; α-stable distribution; generalized hyperbolic distribution

Short-term electricity price forecasting with time series models: A review and evaluation

We investigate the forecasting power of different time series models for electricity spot prices. The models include different specifications of linear autoregressive time series with heteroscedastic noise and/or additional fundamental variables and non-linear regime-switching TAR-type models. The models are tested on a time series of hourly system prices and loads from the California power market. Data from the period July 5, 1999 - April 2, 2000 are used for calibration and from the period April 3 - December 3, 2000 for out-of-sample testing.Electricity price forecasting; Autoregression (AR) model; Threshold Autoregression (TAR) model; Electricity load;

Heavy-tailed distributions in VaR calculations

The essence of the Value-at-Risk (VaR) and Expected Shortfall (ES) computations is estimation of low quantiles in the portfolio return distributions. Hence, the performance of market risk measurement methods depends on the quality of distributional assumptions on the underlying risk factors. This chapter is intended as a guide to heavy-tailed models for VaR-type calculations. We first describe stable laws and their lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Next we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Then we discuss copulas, which enable us to construct a multivariate distribution function from the marginal (possibly different) distribution functions of n individual asset returns in a way that takes their dependence structure into account. This dependence structure may be no longer measured by correlation, but by other adequate functions like rank correlation, comonotonicity or tail dependence. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Parameter estimation; Value-at-Risk (VaR); Expected Shortfall (ES); Copula; Filtered historical simulation (FHS);

Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models

This empirical paper compares the accuracy of 12 time series methods for short-term (day-ahead) spot price forecasting in auction-type electricity markets. The methods considered include standard autoregression (AR) models, their extensions – spike preprocessed, threshold and semiparametric autoregressions (i.e. AR models with nonparametric innovations), as well as, mean-reverting jump diffusions. The methods are compared using a time series of hourly spot prices and system-wide loads for California and a series of hourly spot prices and air temperatures for the Nordic market. We find evidence that (i) models with system load as the exogenous variable generally perform better than pure price models, while this is not necessarily the case when air temperature is considered as the exogenous variable, and that (ii) semiparametric models generally lead to better point and interval forecasts than their competitors, more importantly, they have the potential to perform well under diverse market conditions.Electricity market, Price forecast, Autoregressive model, Nonparametric maximum likelihood, Interval forecast, Conditional coverage

Point and interval forecasting of wholesale electricity prices: Evidence from the Nord Pool market

In this paper we assess the short-term forecasting power of different time series models in the Nord Pool electricity spot market. We evaluate the accuracy of both point and interval predictions; the latter are specifically important for risk management purposes where one is more interested in predicting intervals for future price movements than simply point estimates. We find evidence that non-linear regime-switching models outperform their linear counterparts and that the interval forecasts of all models are overestimated in the relatively non-volatile periods.Wholesale electricity price; Point forecast; Interval forecast; AR model; Threshold AR model

Modeling and forecasting electricity loads: A comparison

In this paper we study two statistical approaches to load forecasting. Both of them model electricity load as a sum of two components – a deterministic (representing seasonalities) and a stochastic (representing noise). They differ in the choice of the seasonality reduction method. Model A utilizes differencing, while Model B uses a recently developed seasonal volatility technique. In both models the stochastic component is described by an ARMA time series. Models are tested on a time series of system-wide loads from the California power market and compared with the official forecast of the California System Operator (CAISO).Electricity, load forecasting, ARMA model, seasonal component

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation;

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black- Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation