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

  • Mikael Bask


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

  • Tung Liu


    (Department of Economics, Ball State University)

  • Anna Widerberg


    (Department of Economics,)

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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Paper provided by Ball State University, Department of Economics in its series Working Papers with number 200603.

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Length: 14 pages
Date of creation: Apr 2006
Date of revision: Apr 2006
Publication status: Published in Physica A, 2007, vol. 376, pp. 565-572
Handle: RePEc:bsu:wpaper:200603
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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. 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.
  3. Mototsugu Shintani & Oliver Linton, 2002. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," LSE Research Online Documents on Economics 2093, London School of Economics and Political Science, LSE Library.
  4. 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.
  5. 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.
  6. 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.
  7. 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..
  8. 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.
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