Modelling Prices in Competitive Electricity Markets
Herausgeber: Bunn, Derek W
Modelling Prices in Competitive Electricity Markets
Herausgeber: Bunn, Derek W
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Electricity markets are structurally different to other commodities, and the real-time dynamic balancing of the electricity network involves many external factors. Because of this, it is not a simple matter to transfer conventional models of financial time series analysis to wholesale electricity prices. The rationale for this compilation of chapters from international authors is, therefore, to provide econometric analysis of wholesale power markets around the world, to give greater understanding of their particular characteristics, and to assess the applicability of various methods of price…mehr
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Electricity markets are structurally different to other commodities, and the real-time dynamic balancing of the electricity network involves many external factors. Because of this, it is not a simple matter to transfer conventional models of financial time series analysis to wholesale electricity prices. The rationale for this compilation of chapters from international authors is, therefore, to provide econometric analysis of wholesale power markets around the world, to give greater understanding of their particular characteristics, and to assess the applicability of various methods of price modelling. Researchers and professionals in this sector will find the book an invaluable guide to the most important state-of-the-art modelling techniques which are converging to define the special approaches necessary for unravelling and forecasting the behaviour of electricity prices. It is a high-quality synthesis of the work of financial engineering, industrial economics and power systems analysis, as they relate to the behaviour of competitive electricity markets.
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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley
- Seitenzahl: 360
- Erscheinungstermin: 2. April 2004
- Englisch
- Abmessung: 250mm x 175mm x 24mm
- Gewicht: 802g
- ISBN-13: 9780470848609
- ISBN-10: 047084860X
- Artikelnr.: 12338195
- Verlag: Wiley
- Seitenzahl: 360
- Erscheinungstermin: 2. April 2004
- Englisch
- Abmessung: 250mm x 175mm x 24mm
- Gewicht: 802g
- ISBN-13: 9780470848609
- ISBN-10: 047084860X
- Artikelnr.: 12338195
DEREK W. BUNN is currently Professor and Chairman of the Decision Sciences subject area and Director of the Energy MarketsGroup at the London Business School, having held previous appointments at Oxford and Stanford universities. As a prominent international advisor on energy economics, he has consulted formany global energy companies and advised a number of government agencies. Author of over 150 research papers and 9 books in theareas of forecasting, decision analysis and energy economics, hehas also been chief editor of the Journal of Forecasting since 1984. His research and practical involvement with the electricity sector extends back over 25 years experience.
List of Contributors.
Preface.
1 Structural and Behavioural Foundations of Competitive Electricity Prices
(Derek W. Bunn).
PART I: PRICES AND STRATEGIC COMPETITION.
2 Competitors? Response Representation for Market Simulation in the Spanish
Daily Market (Efraim Centeno Hernáez, Julián Barquín Gil, José Ignacio de
la Fuente León, Antonio Muñoz San Roque, Mariano J. Ventosa Rodríguez,
Javier García González, Alicia Mateo González, and Agustín Martín
Calmarza).
2.1 Introduction.
2.2 Hourly bidding-based Spanish electricity markets.
2.3 A two-phase clustering procedure for the analysis of bid functions.
2.4 Forecasting methods for residual demand functions using time series
(ARIMA) models.
2.5 Discovering electricity market states for forecasting the residual
demand function using input?output hidden Markov models.
2.6 Conjectural variations approach for modelling electricity markets.
2.7 Conclusions.
Appendix: Nomenclature.
References.
3 Complementarity-Based Equilibrium Modeling for Electric Power Markets
(Benjamin F. Hobbs and Udi Helman).
3.1 Introduction.
3.2 Definitions.
3.3 A general complementarity-based model of energy commodity markets.
3.4 A comparison of two approaches to modeling Cournot generators on a
transmission network.
3.5 A large-scale application: the North American Eastern Interconnection.
3.6 Conclusion.
Acknowledgments.
References.
4 Price Impact of Horizontal Mergers in the British Generation Market
(John Bower).
4.1 Introduction.
4.2 England and Wales wholesale electricity market.
4.3 Analysis.
4.4 Price forecast.
General references.
Ofgem references.
PART II: SPOT MARKET DYNAMICS.
5 Testing for Weekly Seasonal Unit Roots in the Spanish Power Pool (Angel
Le¿on and Antonio Rubia).
5.1 Introduction.
5.2 Data.
5.3 Testing for seasonal unit roots.
5.4 Concluding remarks.
Appendix A: Prewhitening procedure.
Appendix B: Critical values of the HEGY test.
Acknowledgements.
References.
6 Nonlinear Time Series Analysis of Alberta?s Deregulated Electricity
Market (Apostolos Serletis and Ioannis Andreadis).
6.1 Introduction.
6.2 A noise model.
6.3 A multifractal formalism setting.
6.4 On turbulent behavior.
6.5 On nonlinearity.
6.6 On chaos.
6.7 Conclusion.
Acknowledgments.
References.
7 Quantile-Based Probabilistic Models for Electricity Prices (Shi-Jie Deng
and Wenjiang Jiang).
7.1 Introduction.
7.2 Quantile-based distributions and the modelling of marginal
distributions of electricity price. 7.3 Quantile-GARCH models and the
modelling of time series of electricity price.
7.4 Parameter Inference.
7.5 Conclusion.
Acknowledgements.
References.
8 Forecasting Time-Varying Covariance Matrices in the Intradaily Spot
Market of Argentina (Angel León and Antonio Rubia).
8.1 Introduction.
8.2 VAR analysis for block bids.
8.3 Modelling the conditional covariance matrix.
8.4 Forecasting conditional covariance matrices.
8.5 Concluding remarks.
Acknowledgements.
References.
PART III: SPATIAL PRICE INTERACTIONS.
9 Identifying Dynamic Interactions in Western US Spot Markets (Christine A.
Jerko, James W. Mjelde and David A. Bessler).
9.1 Introduction.
9.2 Data.
9.3 Methods.
9.4 Results.
9.5 Discussion.
References.
10 Transmission of Prices and Volatility in the Australian Electricity Spot
Markets (Andrew C. Worthington and Helen Higgs).
10.1 Introduction.
10.2 Data and summary statistics.
10.3 Multivariate GARCH model.
10.4 Empirical results.
10.5 Conclusion.
References.
PART IV: FORWARD PRICES.
11 Forecasting Higher Moments of the Power Price Using Medium-Term
Equilibrium Economics and the Value of Security of Supply (Chris Harris).
11.1 Introduction.
11.2 Construction of the moments of price.
11.3 Worked example.
11.4 Commentary.
11.5 Conclusions.
References.
12 Modeling Electricity Forward Curve Dynamics in the Nordic Market
(Nicolas Audet, Pirja Heiskanen, Jussi Keppo and Iivo Vehviläinen).
12.1 Introduction.
12.2 The model.
12.3 Forward model in the Nordic market.
12.4 Model usage examples.
12.5 Conclusion.
Appendix: Estimation of model parameters.
Acknowledgments.
References.
13 The Forward Curve Dynamic and Market Transition Forecasts (Svetlana
Borovkova).
13.1 The term structure of commodity futures prices.
13.2 Forecasting market transitions.
13.3 Critical regions and bootstrap methods.
13.4 Application to electricity and oil futures.
13.5 Concluding remarks.
References.
PART V: FORECASTING AND RISK MANAGEMENT.
14 Price Modelling for Profit at Risk Management (Jacob Lemming).
14.1 Introduction.
14.2 Electricity price modelling.
14.3 A profit at risk risk management model.
14.4 Modelling input parameters.
14.5 Experimental results.
14.6 Conclusions.
References.
15 ForecastingWeather Variable Densities for Weather Derivatives and
Electricity Prices (James W. Taylor).
15.1 Introduction.
15.2 Weather ensemble predictions.
15.3 Univariate time series modelling of weather variables.
15.4 Empirical comparison of weather point forecasts.
15.5 Empirical comparison of weather quantile forecasts.
15.6 Summary of the analysis of temperature, wind speed and cloud cover.
15.7 Forecasting the payoff density for a weather derivative.
15.8 Electricity demand modelling.
15.9 Concluding comments.
References.
Index.
Preface.
1 Structural and Behavioural Foundations of Competitive Electricity Prices
(Derek W. Bunn).
PART I: PRICES AND STRATEGIC COMPETITION.
2 Competitors? Response Representation for Market Simulation in the Spanish
Daily Market (Efraim Centeno Hernáez, Julián Barquín Gil, José Ignacio de
la Fuente León, Antonio Muñoz San Roque, Mariano J. Ventosa Rodríguez,
Javier García González, Alicia Mateo González, and Agustín Martín
Calmarza).
2.1 Introduction.
2.2 Hourly bidding-based Spanish electricity markets.
2.3 A two-phase clustering procedure for the analysis of bid functions.
2.4 Forecasting methods for residual demand functions using time series
(ARIMA) models.
2.5 Discovering electricity market states for forecasting the residual
demand function using input?output hidden Markov models.
2.6 Conjectural variations approach for modelling electricity markets.
2.7 Conclusions.
Appendix: Nomenclature.
References.
3 Complementarity-Based Equilibrium Modeling for Electric Power Markets
(Benjamin F. Hobbs and Udi Helman).
3.1 Introduction.
3.2 Definitions.
3.3 A general complementarity-based model of energy commodity markets.
3.4 A comparison of two approaches to modeling Cournot generators on a
transmission network.
3.5 A large-scale application: the North American Eastern Interconnection.
3.6 Conclusion.
Acknowledgments.
References.
4 Price Impact of Horizontal Mergers in the British Generation Market
(John Bower).
4.1 Introduction.
4.2 England and Wales wholesale electricity market.
4.3 Analysis.
4.4 Price forecast.
General references.
Ofgem references.
PART II: SPOT MARKET DYNAMICS.
5 Testing for Weekly Seasonal Unit Roots in the Spanish Power Pool (Angel
Le¿on and Antonio Rubia).
5.1 Introduction.
5.2 Data.
5.3 Testing for seasonal unit roots.
5.4 Concluding remarks.
Appendix A: Prewhitening procedure.
Appendix B: Critical values of the HEGY test.
Acknowledgements.
References.
6 Nonlinear Time Series Analysis of Alberta?s Deregulated Electricity
Market (Apostolos Serletis and Ioannis Andreadis).
6.1 Introduction.
6.2 A noise model.
6.3 A multifractal formalism setting.
6.4 On turbulent behavior.
6.5 On nonlinearity.
6.6 On chaos.
6.7 Conclusion.
Acknowledgments.
References.
7 Quantile-Based Probabilistic Models for Electricity Prices (Shi-Jie Deng
and Wenjiang Jiang).
7.1 Introduction.
7.2 Quantile-based distributions and the modelling of marginal
distributions of electricity price. 7.3 Quantile-GARCH models and the
modelling of time series of electricity price.
7.4 Parameter Inference.
7.5 Conclusion.
Acknowledgements.
References.
8 Forecasting Time-Varying Covariance Matrices in the Intradaily Spot
Market of Argentina (Angel León and Antonio Rubia).
8.1 Introduction.
8.2 VAR analysis for block bids.
8.3 Modelling the conditional covariance matrix.
8.4 Forecasting conditional covariance matrices.
8.5 Concluding remarks.
Acknowledgements.
References.
PART III: SPATIAL PRICE INTERACTIONS.
9 Identifying Dynamic Interactions in Western US Spot Markets (Christine A.
Jerko, James W. Mjelde and David A. Bessler).
9.1 Introduction.
9.2 Data.
9.3 Methods.
9.4 Results.
9.5 Discussion.
References.
10 Transmission of Prices and Volatility in the Australian Electricity Spot
Markets (Andrew C. Worthington and Helen Higgs).
10.1 Introduction.
10.2 Data and summary statistics.
10.3 Multivariate GARCH model.
10.4 Empirical results.
10.5 Conclusion.
References.
PART IV: FORWARD PRICES.
11 Forecasting Higher Moments of the Power Price Using Medium-Term
Equilibrium Economics and the Value of Security of Supply (Chris Harris).
11.1 Introduction.
11.2 Construction of the moments of price.
11.3 Worked example.
11.4 Commentary.
11.5 Conclusions.
References.
12 Modeling Electricity Forward Curve Dynamics in the Nordic Market
(Nicolas Audet, Pirja Heiskanen, Jussi Keppo and Iivo Vehviläinen).
12.1 Introduction.
12.2 The model.
12.3 Forward model in the Nordic market.
12.4 Model usage examples.
12.5 Conclusion.
Appendix: Estimation of model parameters.
Acknowledgments.
References.
13 The Forward Curve Dynamic and Market Transition Forecasts (Svetlana
Borovkova).
13.1 The term structure of commodity futures prices.
13.2 Forecasting market transitions.
13.3 Critical regions and bootstrap methods.
13.4 Application to electricity and oil futures.
13.5 Concluding remarks.
References.
PART V: FORECASTING AND RISK MANAGEMENT.
14 Price Modelling for Profit at Risk Management (Jacob Lemming).
14.1 Introduction.
14.2 Electricity price modelling.
14.3 A profit at risk risk management model.
14.4 Modelling input parameters.
14.5 Experimental results.
14.6 Conclusions.
References.
15 ForecastingWeather Variable Densities for Weather Derivatives and
Electricity Prices (James W. Taylor).
15.1 Introduction.
15.2 Weather ensemble predictions.
15.3 Univariate time series modelling of weather variables.
15.4 Empirical comparison of weather point forecasts.
15.5 Empirical comparison of weather quantile forecasts.
15.6 Summary of the analysis of temperature, wind speed and cloud cover.
15.7 Forecasting the payoff density for a weather derivative.
15.8 Electricity demand modelling.
15.9 Concluding comments.
References.
Index.
List of Contributors.
Preface.
1 Structural and Behavioural Foundations of Competitive Electricity Prices
(Derek W. Bunn).
PART I: PRICES AND STRATEGIC COMPETITION.
2 Competitors? Response Representation for Market Simulation in the Spanish
Daily Market (Efraim Centeno Hernáez, Julián Barquín Gil, José Ignacio de
la Fuente León, Antonio Muñoz San Roque, Mariano J. Ventosa Rodríguez,
Javier García González, Alicia Mateo González, and Agustín Martín
Calmarza).
2.1 Introduction.
2.2 Hourly bidding-based Spanish electricity markets.
2.3 A two-phase clustering procedure for the analysis of bid functions.
2.4 Forecasting methods for residual demand functions using time series
(ARIMA) models.
2.5 Discovering electricity market states for forecasting the residual
demand function using input?output hidden Markov models.
2.6 Conjectural variations approach for modelling electricity markets.
2.7 Conclusions.
Appendix: Nomenclature.
References.
3 Complementarity-Based Equilibrium Modeling for Electric Power Markets
(Benjamin F. Hobbs and Udi Helman).
3.1 Introduction.
3.2 Definitions.
3.3 A general complementarity-based model of energy commodity markets.
3.4 A comparison of two approaches to modeling Cournot generators on a
transmission network.
3.5 A large-scale application: the North American Eastern Interconnection.
3.6 Conclusion.
Acknowledgments.
References.
4 Price Impact of Horizontal Mergers in the British Generation Market
(John Bower).
4.1 Introduction.
4.2 England and Wales wholesale electricity market.
4.3 Analysis.
4.4 Price forecast.
General references.
Ofgem references.
PART II: SPOT MARKET DYNAMICS.
5 Testing for Weekly Seasonal Unit Roots in the Spanish Power Pool (Angel
Le¿on and Antonio Rubia).
5.1 Introduction.
5.2 Data.
5.3 Testing for seasonal unit roots.
5.4 Concluding remarks.
Appendix A: Prewhitening procedure.
Appendix B: Critical values of the HEGY test.
Acknowledgements.
References.
6 Nonlinear Time Series Analysis of Alberta?s Deregulated Electricity
Market (Apostolos Serletis and Ioannis Andreadis).
6.1 Introduction.
6.2 A noise model.
6.3 A multifractal formalism setting.
6.4 On turbulent behavior.
6.5 On nonlinearity.
6.6 On chaos.
6.7 Conclusion.
Acknowledgments.
References.
7 Quantile-Based Probabilistic Models for Electricity Prices (Shi-Jie Deng
and Wenjiang Jiang).
7.1 Introduction.
7.2 Quantile-based distributions and the modelling of marginal
distributions of electricity price. 7.3 Quantile-GARCH models and the
modelling of time series of electricity price.
7.4 Parameter Inference.
7.5 Conclusion.
Acknowledgements.
References.
8 Forecasting Time-Varying Covariance Matrices in the Intradaily Spot
Market of Argentina (Angel León and Antonio Rubia).
8.1 Introduction.
8.2 VAR analysis for block bids.
8.3 Modelling the conditional covariance matrix.
8.4 Forecasting conditional covariance matrices.
8.5 Concluding remarks.
Acknowledgements.
References.
PART III: SPATIAL PRICE INTERACTIONS.
9 Identifying Dynamic Interactions in Western US Spot Markets (Christine A.
Jerko, James W. Mjelde and David A. Bessler).
9.1 Introduction.
9.2 Data.
9.3 Methods.
9.4 Results.
9.5 Discussion.
References.
10 Transmission of Prices and Volatility in the Australian Electricity Spot
Markets (Andrew C. Worthington and Helen Higgs).
10.1 Introduction.
10.2 Data and summary statistics.
10.3 Multivariate GARCH model.
10.4 Empirical results.
10.5 Conclusion.
References.
PART IV: FORWARD PRICES.
11 Forecasting Higher Moments of the Power Price Using Medium-Term
Equilibrium Economics and the Value of Security of Supply (Chris Harris).
11.1 Introduction.
11.2 Construction of the moments of price.
11.3 Worked example.
11.4 Commentary.
11.5 Conclusions.
References.
12 Modeling Electricity Forward Curve Dynamics in the Nordic Market
(Nicolas Audet, Pirja Heiskanen, Jussi Keppo and Iivo Vehviläinen).
12.1 Introduction.
12.2 The model.
12.3 Forward model in the Nordic market.
12.4 Model usage examples.
12.5 Conclusion.
Appendix: Estimation of model parameters.
Acknowledgments.
References.
13 The Forward Curve Dynamic and Market Transition Forecasts (Svetlana
Borovkova).
13.1 The term structure of commodity futures prices.
13.2 Forecasting market transitions.
13.3 Critical regions and bootstrap methods.
13.4 Application to electricity and oil futures.
13.5 Concluding remarks.
References.
PART V: FORECASTING AND RISK MANAGEMENT.
14 Price Modelling for Profit at Risk Management (Jacob Lemming).
14.1 Introduction.
14.2 Electricity price modelling.
14.3 A profit at risk risk management model.
14.4 Modelling input parameters.
14.5 Experimental results.
14.6 Conclusions.
References.
15 ForecastingWeather Variable Densities for Weather Derivatives and
Electricity Prices (James W. Taylor).
15.1 Introduction.
15.2 Weather ensemble predictions.
15.3 Univariate time series modelling of weather variables.
15.4 Empirical comparison of weather point forecasts.
15.5 Empirical comparison of weather quantile forecasts.
15.6 Summary of the analysis of temperature, wind speed and cloud cover.
15.7 Forecasting the payoff density for a weather derivative.
15.8 Electricity demand modelling.
15.9 Concluding comments.
References.
Index.
Preface.
1 Structural and Behavioural Foundations of Competitive Electricity Prices
(Derek W. Bunn).
PART I: PRICES AND STRATEGIC COMPETITION.
2 Competitors? Response Representation for Market Simulation in the Spanish
Daily Market (Efraim Centeno Hernáez, Julián Barquín Gil, José Ignacio de
la Fuente León, Antonio Muñoz San Roque, Mariano J. Ventosa Rodríguez,
Javier García González, Alicia Mateo González, and Agustín Martín
Calmarza).
2.1 Introduction.
2.2 Hourly bidding-based Spanish electricity markets.
2.3 A two-phase clustering procedure for the analysis of bid functions.
2.4 Forecasting methods for residual demand functions using time series
(ARIMA) models.
2.5 Discovering electricity market states for forecasting the residual
demand function using input?output hidden Markov models.
2.6 Conjectural variations approach for modelling electricity markets.
2.7 Conclusions.
Appendix: Nomenclature.
References.
3 Complementarity-Based Equilibrium Modeling for Electric Power Markets
(Benjamin F. Hobbs and Udi Helman).
3.1 Introduction.
3.2 Definitions.
3.3 A general complementarity-based model of energy commodity markets.
3.4 A comparison of two approaches to modeling Cournot generators on a
transmission network.
3.5 A large-scale application: the North American Eastern Interconnection.
3.6 Conclusion.
Acknowledgments.
References.
4 Price Impact of Horizontal Mergers in the British Generation Market
(John Bower).
4.1 Introduction.
4.2 England and Wales wholesale electricity market.
4.3 Analysis.
4.4 Price forecast.
General references.
Ofgem references.
PART II: SPOT MARKET DYNAMICS.
5 Testing for Weekly Seasonal Unit Roots in the Spanish Power Pool (Angel
Le¿on and Antonio Rubia).
5.1 Introduction.
5.2 Data.
5.3 Testing for seasonal unit roots.
5.4 Concluding remarks.
Appendix A: Prewhitening procedure.
Appendix B: Critical values of the HEGY test.
Acknowledgements.
References.
6 Nonlinear Time Series Analysis of Alberta?s Deregulated Electricity
Market (Apostolos Serletis and Ioannis Andreadis).
6.1 Introduction.
6.2 A noise model.
6.3 A multifractal formalism setting.
6.4 On turbulent behavior.
6.5 On nonlinearity.
6.6 On chaos.
6.7 Conclusion.
Acknowledgments.
References.
7 Quantile-Based Probabilistic Models for Electricity Prices (Shi-Jie Deng
and Wenjiang Jiang).
7.1 Introduction.
7.2 Quantile-based distributions and the modelling of marginal
distributions of electricity price. 7.3 Quantile-GARCH models and the
modelling of time series of electricity price.
7.4 Parameter Inference.
7.5 Conclusion.
Acknowledgements.
References.
8 Forecasting Time-Varying Covariance Matrices in the Intradaily Spot
Market of Argentina (Angel León and Antonio Rubia).
8.1 Introduction.
8.2 VAR analysis for block bids.
8.3 Modelling the conditional covariance matrix.
8.4 Forecasting conditional covariance matrices.
8.5 Concluding remarks.
Acknowledgements.
References.
PART III: SPATIAL PRICE INTERACTIONS.
9 Identifying Dynamic Interactions in Western US Spot Markets (Christine A.
Jerko, James W. Mjelde and David A. Bessler).
9.1 Introduction.
9.2 Data.
9.3 Methods.
9.4 Results.
9.5 Discussion.
References.
10 Transmission of Prices and Volatility in the Australian Electricity Spot
Markets (Andrew C. Worthington and Helen Higgs).
10.1 Introduction.
10.2 Data and summary statistics.
10.3 Multivariate GARCH model.
10.4 Empirical results.
10.5 Conclusion.
References.
PART IV: FORWARD PRICES.
11 Forecasting Higher Moments of the Power Price Using Medium-Term
Equilibrium Economics and the Value of Security of Supply (Chris Harris).
11.1 Introduction.
11.2 Construction of the moments of price.
11.3 Worked example.
11.4 Commentary.
11.5 Conclusions.
References.
12 Modeling Electricity Forward Curve Dynamics in the Nordic Market
(Nicolas Audet, Pirja Heiskanen, Jussi Keppo and Iivo Vehviläinen).
12.1 Introduction.
12.2 The model.
12.3 Forward model in the Nordic market.
12.4 Model usage examples.
12.5 Conclusion.
Appendix: Estimation of model parameters.
Acknowledgments.
References.
13 The Forward Curve Dynamic and Market Transition Forecasts (Svetlana
Borovkova).
13.1 The term structure of commodity futures prices.
13.2 Forecasting market transitions.
13.3 Critical regions and bootstrap methods.
13.4 Application to electricity and oil futures.
13.5 Concluding remarks.
References.
PART V: FORECASTING AND RISK MANAGEMENT.
14 Price Modelling for Profit at Risk Management (Jacob Lemming).
14.1 Introduction.
14.2 Electricity price modelling.
14.3 A profit at risk risk management model.
14.4 Modelling input parameters.
14.5 Experimental results.
14.6 Conclusions.
References.
15 ForecastingWeather Variable Densities for Weather Derivatives and
Electricity Prices (James W. Taylor).
15.1 Introduction.
15.2 Weather ensemble predictions.
15.3 Univariate time series modelling of weather variables.
15.4 Empirical comparison of weather point forecasts.
15.5 Empirical comparison of weather quantile forecasts.
15.6 Summary of the analysis of temperature, wind speed and cloud cover.
15.7 Forecasting the payoff density for a weather derivative.
15.8 Electricity demand modelling.
15.9 Concluding comments.
References.
Index.