Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach

This book offers an in-depth and up-to-date review of different statistical tools that can be used to analyze and forecast the dynamics of two crucial for every energy company processes—electricity prices and loads. It provides coverage of seasonal decomposition, mean reversion, heavy-tailed distributions, exponential smoothing, spike preprocessing, autoregressive time series including models with exogenous variables and heteroskedastic (GARCH) components, regime-switching models, interval forecasts, jump-diffusion models, derivatives pricing and the market price of risk. Modeling and Forecasting Electricity Loads and Prices is packaged with a CD containing both the data and detailed examples of implementation of different techniques in Matlab, with additional examples in SAS. A reader can retrace all the intermediate steps of a practical implementation of a model and test his understanding of the method and correctness of the computer code using the same input data. The book will be of particular interest to the quants employed by the utilities, independent power generators and marketers, energy trading desks of the hedge funds and financial institutions, and the executives attending courses designed to help them to brush up on their technical skills. The text will be also of use to graduate students in electrical engineering, econometrics and finance wanting to get a grip on advanced statistical tools applied in this hot area. In fact, there are sixteen Case Studies in the book making it a self-contained tutorial to electricity load and price modeling and forecasting.

Table of Contents:
Preface ix Acknowledgments xiii 1 Complex Electricity Markets 1 1.1 Liberalization 1 1.2 The Marketplace 3 1.2.1 Power Pools and Power Exchanges 3 1.2.2 Nodal and Zonal Pricing 6 1.2.3 Market Structure 7 1.2.4 Traded Products 7 1.3 Europe 9 1.3.1 The England and Wales Electricity Market 9 1.3.2 The Nordic Market 11 1.3.3 Price Setting at Nord Pool 11 1.3.4 Continental Europe 13 1.4 North America 18 1.4.1 PJM Interconnection 19 1.4.2 California and the Electricity Crisis 20 1.4.3 Alberta and Ontario 21 1.5 Australia and New Zealand 22 1.6 Summary 23 1.7 Further Reading 23 2 Stylized Facts of Electricity Loads and Prices 25 2.1 Introduction 25 2.2 Price Spikes 25 2.2.1 Case Study: The June 1998 Cinergy Price Spike 28 2.2.2 When Supply Meets Demand 29 2.2.3 What is Causing the Spikes? 32 2.2.4 The Definition 32 2.3 Seasonality 32 2.3.1 Measuring Serial Correlation 36 2.3.2 Spectral Analysis and the Periodogram 39 2.3.3 Case Study: Seasonal Behavior of Electricity Prices and Loads 40 2.4 Seasonal Decomposition 41 2.4.1 Differencing 42 2.4.2 Mean or Median Week 44 2.4.3 Moving Average Technique 44 2.4.4 Annual Seasonality and Spectral Decomposition 44 2.4.5 Rolling Volatility Technique 45 2.4.6 Case Study: Rolling Volatility in Practice 46 2.4.7 Wavelet Decomposition 47 2.4.8 Case Study: Wavelet Filtering of Nord Pool Hourly System Prices 49 2.5 Mean Reversion 49 2.5.1 R/S Analysis 50 2.5.2 Detrended Fluctuation Analysis 52 2.5.3 Periodogram Regression 53 2.5.4 Average Wavelet Coefficient 53 2.5.5 Case Study: Anti-persistence of Electricity Prices 54 2.6 Distributions of Electricity Prices 56 2.6.1 Stable Distributions 56 2.6.2 Hyperbolic Distributions 58 2.6.3 Case Study: Distribution of EEX Spot Prices 59 2.6.4 Further Empirical Evidence and Possible Applications 62 2.7 Summary 64 2.8 Further Reading 64 3 Modeling and Forecasting Electricity Loads 67 3.1 Introduction 67 3.2 Factors Affecting Load Patterns 69 3.2.1 Case Study: Dealing with Missing Values and Outliers 69 3.2.2 Time Factors 71 3.2.3 Weather Conditions 71 3.2.4 Case Study: California Weather vs Load 72 3.2.5 Other Factors 74 3.3 Overview of Artificial Intelligence-Based Methods 75 3.4 Statistical Methods 78 3.4.1 Similar-Day Method 79 3.4.2 Exponential Smoothing 79 3.4.3 Regression Methods 81 3.4.4 Autoregressive Model 82 3.4.5 Autoregressive Moving Average Model 83 3.4.6 ARMA Model Identification 84 3.4.7 Case Study: Modeling Daily Loads in California 86 3.4.8 Autoregressive Integrated Moving Average Model 95 3.4.9 Time Series Models with Exogenous Variables 97 3.4.10 Case Study: Modeling Daily Loads in California with Exogenous Variables 98 3.5 Summary 100 3.6 Further Reading 100 4 Modeling and Forecasting Electricity Prices 101 4.1 Introduction 101 4.2 Overview of Modeling Approaches 102 4.3 Statistical Methods and Price Forecasting 106 4.3.1 Exogenous Factors 106 4.3.2 Spike Preprocessing 107 4.3.3 How to Assess the Quality of Price Forecasts 107 4.3.4 ARMA-type Models 109 4.3.5 Time Series Models with Exogenous Variables 111 4.3.6 Autoregressive GARCH Models 113 4.3.7 Case Study: Forecasting Hourly CalPX Spot Prices with Linear Models 114 4.3.8 Case Study: Is Spike Preprocessing Advantageous? 125 4.3.9 Regime-Switching Models 127 4.3.10 Calibration of Regime-Switching Models 132 4.3.11 Case Study: Forecasting Hourly CalPX Spot Prices with Regime-Switching Models 132 4.3.12 Interval Forecasts 136 4.4 Quantitative Models and Derivatives Valuation 136 4.4.1 Jump-Diffusion Models 137 4.4.2 Calibration of Jump-Diffusion Models 139 4.4.3 Case Study: A Mean-Reverting Jump-Diffusion Model for Nord Pool Spot Prices 140 4.4.4 Hybrid Models 143 4.4.5 Case Study: Regime-Switching Models for Nord Pool Spot Prices 144 4.4.6 Hedging and the Use of Derivatives 147 4.4.7 Derivatives Pricing and the Market Price of Risk 148 4.4.8 Case Study: Asian-Style Electricity Options 150 4.5 Summary 153 4.6 Further Reading 154 Bibliography 157 Subject Index 171