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The stability of electricity prices: estimation and inference of the Lyapunov exponents

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Author Info

  • Bask , Mikael

    () (Bank of Finland Research)

  • Liu , Tung

    () (Department of Economics, Ball State University)

  • Widerberg , Anna

    () (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.

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File URL: http://www.suomenpankki.fi/en/julkaisut/tutkimukset/keskustelualoitteet/Documents/0609netti.pdf
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Bibliographic Info

Paper provided by Bank of Finland in its series Research Discussion Papers with number 9/2006.

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Length: 23 pages
Date of creation: 12 Jun 2006
Date of revision:
Handle: RePEc:hhs:bofrdp:2006_009

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Postal: Bank of Finland, P.O. Box 160, FI-00101 Helsinki, Finland
Web page: http://www.suomenpankki.fi/en/
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Keywords: feedforward neural network; Nord Pool; Lyapunov exponents; spot electricity prices; stochastic dynamic system;

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References

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  1. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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..
  7. 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.
  8. 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.
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Citations

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Cited by:
  1. Bask, Mikael, 2007. "Measuring potential market risk," Research Discussion Papers 20/2007, Bank of Finland.
  2. 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.
  3. 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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