The stability of electricity prices: estimation and inference of the Lyapunov exponents
AbstractThe aim of this paper is to illustrate how the stability of a stochastic dynamic system is measured using the Lyapunov exponents. Specifically, we use a feedforward neural network to estimate these exponents as well as asymptotic results for this estimator to test for unstable (chaotic) dynamics. The data set used is spot electricity prices from the Nordic power exchange market. Nord Pool, and the dynamic system that generates these prices appears to be chaotic in one case.
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Bibliographic InfoPaper provided by Bank of Finland in its series Research Discussion Papers with number 9/2006.
Length: 23 pages
Date of creation: 12 Jun 2006
Date of revision:
feedforward neural network; Nord Pool; Lyapunov exponents; spot electricity prices; stochastic dynamic system;
Other versions of this item:
- Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
- Mikael Bask & Tung Liu & Anna Widerberg, 2006. "The Stability of Electricity Prices: Estimation and Inference of the Lyapunov Exponent," Working Papers 200603, Ball State University, Department of Economics, revised Apr 2006.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-10-21 (All new papers)
- NEP-CMP-2006-10-21 (Computational Economics)
- NEP-ECM-2006-10-21 (Econometrics)
- NEP-ENE-2006-10-21 (Energy Economics)
- NEP-MIC-2006-10-21 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mototsugu Shintani & Oliver Linton, 2003.
"Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos,"
Vanderbilt University Department of Economics Working Papers
0309, Vanderbilt University Department of Economics.
- Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
- Oliver Linton & Mototsugu Shintani, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2003/455, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Oliver Linton & Mototsugu Shintani, 2002. "Nonparametric Neutral Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2002/434, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Bask, Mikael & de Luna, Xavier, 2001.
"Characterizing the degree of stability of non-linear dynamic models,"
UmeÃ¥ Economic Studies
564, Umeå University, Department of Economics.
- Bask Mikael & de Luna Xavier, 2002. "Characterizing the Degree of Stability of Non-linear Dynamic Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(1), pages 1-19, April.
- Simon M. Potter, 1999.
"Nonlinear impulse response functions,"
65, Federal Reserve Bank of New York.
- Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S41-60, Suppl. De.
- Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
- Andrews, Donald W K, 1991.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Econometric Society, vol. 59(3), pages 817-58, May.
- Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Kuan, Chung-Ming & Liu, Tung, 1995. "Forecasting Exchange Rates Using Feedforward and Recurrent Neural Networks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 347-64, Oct.-Dec..
- Bask, Mikael & de Luna, Xavier, 2001. "EMU and the Stability and Volatility of Foreign Exchange: Some Empirical Evidence," UmeÃ¥ Economic Studies 565, Umeå University, Department of Economics.
- Bask, Mikael, 2007.
"Measuring potential market risk,"
Research Discussion Papers
20/2007, Bank of Finland.
- Bask, Mikael & Widerberg, Anna, 2009.
"Market structure and the stability and volatility of electricity prices,"
Elsevier, vol. 31(2), pages 278-288, March.
- Bask, Mikael & Widerberg, Anna, 2008. "Market Structure and the Stability and Volatility of Electricity Prices," Working Papers in Economics 327, University of Gothenburg, Department of Economics.
- Bask, Mikael & Widerberg, Anna, 2007. "The Stability and Volatility of Electricity Prices: An Illustration of (lambda, sigma-2) Analysis," Working Papers in Economics 267, University of Gothenburg, Department of Economics.
- G. Papaioannou & P. Papaioannou & N. Parliaris, 2014. "Modeling the stylized facts of wholesale system marginal price (SMP) and the impacts of regulatory reforms on the Greek Electricity Market," Papers 1401.5452, arXiv.org.
- Giabardo, Paolo & Zugno, Marco & Pinson, Pierre & Madsen, Henrik, 2010. "Feedback, competition and stochasticity in a day ahead electricity market," Energy Economics, Elsevier, vol. 32(2), pages 292-301, March.
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