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The Stability of Electricity Prices: Estimation and Inference of the Lyapunov Exponent

Author

Listed:
  • Mikael Bask

    () (Monetary Policy and Research Department, Bank of Finland,)

  • Tung Liu

    () (Department of Economics, Ball State University)

  • Anna Widerberg

    () (Department of Economics,)

Abstract

The 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.

Suggested Citation

  • 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.
  • Handle: RePEc:bsu:wpaper:200603
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    File URL: http://web.bsu.edu/cob/econ/research/papers/bsuecwp200603bask.pdf
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    References listed on IDEAS

    as
    1. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
    2. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, pages 1-33.
    3. Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 1-12.
    4. Bask, Mikael & de Luna, Xavier, 2001. "Characterizing the degree of stability of non-linear dynamic models," Umeå Economic Studies 564, Umeå University, Department of Economics.
    5. 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 41-60, Suppl. De.
    6. Bask Mikael & de Luna Xavier, 2002. "Characterizing the Degree of Stability of Non-linear Dynamic Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, pages 1-19.
    7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, pages 817-858.
    8. 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 347-364, Oct.-Dec..
    9. Bask, Mikael & de Luna, Xavier, 2001. "EMU and the Stability and Volatility of Foreign Exchange: Some Empirical Evidence," Umeå Economic Studies 565, Umeå University, Department of Economics.
    10. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, pages 119-147.
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    Citations

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    Cited by:

    1. 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.
    2. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, pages 180-186.
    3. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, pages 278-288.
    4. Jokipii, Terhi & Lucey, Brian, 2006. "Contagion and interdependence: measuring CEE banking sector co-movements," Research Discussion Papers 15/2006, Bank of Finland.
    5. Bask, Mikael, 2007. "Measuring potential market risk," Research Discussion Papers 20/2007, Bank of Finland.
    6. Giabardo, Paolo & Zugno, Marco & Pinson, Pierre & Madsen, Henrik, 2010. "Feedback, competition and stochasticity in a day ahead electricity market," Energy Economics, Elsevier, pages 292-301.
    7. Coria, Jessica & Sterner, Thomas, 2008. "Tradable Permits in Developing Countries: Evidence from Air Pollution in Santiago, Chile," Discussion Papers dp-08-51, Resources For the Future.
    8. Andrén, Thomas, 2007. "The Persistence of Welfare Participation," IZA Discussion Papers 3100, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Feedforward Neural Network; Nord Pool; Lyapunov Exponents; Spot Electricity Prices; Stochastic Dynamic System;

    JEL classification:

    • 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; Diffusion Processes

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