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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://econfac.bsu.edu/research/workingpapers/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, vol. 120(1), pages 1-33, May.
    3. Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-12, October.
    4. 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.
    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. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Bask, Mikael & de Luna, Xavier, 2005. "EMU and the stability and volatility of foreign exchange: Some empirical evidence," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 737-750.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Wang, Jianzhou & Jia, Ruiling & Zhao, Weigang & Wu, Jie & Dong, Yao, 2012. "Application of the largest Lyapunov exponent and non-linear fractal extrapolation algorithm to short-term load forecasting," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1277-1287.
    2. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    3. Lucía Inglada-Pérez & Pablo Coto-Millán, 2021. "A Chaos Analysis of the Dry Bulk Shipping Market," Mathematics, MDPI, vol. 9(17), pages 1-35, August.
    4. 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.
    5. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    6. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.
    7. Jokipii, Terhi & Lucey, Brian, 2007. "Contagion and interdependence: Measuring CEE banking sector co-movements," Economic Systems, Elsevier, vol. 31(1), pages 71-96, March.
    8. repec:zbw:bofrdp:2006_015 is not listed on IDEAS
    9. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    10. 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.
    11. 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.

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    More about this item

    Keywords

    Feedforward Neural Network; Nord Pool; Lyapunov Exponents; Spot Electricity Prices; Stochastic Dynamic System;
    All these keywords.

    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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