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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)

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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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Publisher 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.bof.fi/en/tutkimus
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Related research
Keywords: feedforward neural network; Nord Pool; Lyapunov exponents; spot electricity prices; stochastic dynamic system;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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.:
  1. Niinimäki, Juha-Pekka & Takalo, Tuomas & Kultti, Klaus, 2006. "The role of comparing in financial markets with hidden information," Research Discussion Papers 1/2006, Bank of Finland. [Downloadable!]
  2. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September. [Downloadable!] (restricted)
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  3. Kilponen, Juha & Ripatti , Antti, 2006. "Labour and product market competition in a small open economy, Simulation results using a DGE model of the Finnish economy," Research Discussion Papers 5/2006, Bank of Finland. [Downloadable!]
  4. 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.. [Downloadable!] (restricted)
  5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  6. Kurt Hornik & Maxwell Stinchcombe & Halbert White, 1990. "Universal Approximation of an Unknown Mapping And Its Derivatives Using Multilayer Feedforward Networks," University of California at San Diego, Economics Working Paper Series 89-36r, Department of Economics, UC San Diego.
  7. 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. [Downloadable!] (restricted)
  8. repec:bep:sndecm:6:2002:1:1002-1002 is not listed on IDEAS
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  9. Bask, Mikael, 2006. "Adaptive learning in an expectational difference equation with several lags: selecting among learnable REE," Research Discussion Papers 7/2006, Bank of Finland. [Downloadable!]
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  10. 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. [Downloadable!] (restricted)
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  11. 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. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Jokipii, Terhi, 2006. "Forecasting market crashes: further international evidence," Research Discussion Papers 22/2006, Bank of Finland. [Downloadable!]
  2. Anandarajan , Asokan & Hasan , Iftekhar & McCarthy , Cornelia, 2006. "The use of loan loss provisions for capital management, earnings management and signalling by Australian banks," Research Discussion Papers 23/2006, Bank of Finland. [Downloadable!]
  3. Marsh , Ian W, 2006. "The effect of lenders’ credit risk transfer activities on borrowing firms’ equity returns," Research Discussion Papers 31/2006, Bank of Finland. [Downloadable!]
  4. Jokivuolle , Esa & Peura , Samu, 2006. "Rating targeting and the confidence levels implicit in bank capital," Research Discussion Papers 27/2006, Bank of Finland. [Downloadable!]
  5. Ravenna , Federico & Seppälä , Juha, 2006. "Monetary policy and rejections of the expectations hypothesis," Research Discussion Papers 25/2006, Bank of Finland. [Downloadable!]
  6. Aalto-Setälä , Ville & Schindler, Robert, 2006. "The importance of attractive prices in pricing dynamics," Research Discussion Papers 30/2006, Bank of Finland. [Downloadable!]
  7. Välimäki , Tuomas, 2006. "Why the marginal MRO rate exceeds the ECB policy rate?," Research Discussion Papers 20/2006, Bank of Finland. [Downloadable!]
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