IDEAS home Printed from https://ideas.repec.org/p/bsu/wpaper/200603.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://econfac.bsu.edu/research/workingpapers/bsuecwp200603bask.pdf
    File Function: First version, 2006
    Download Restriction: no
    ---><---

    Other versions of this item:

    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bask, Mikael & Liu, Tung & Widerberg, Anna, 2007. "The stability of electricity prices: Estimation and inference of the Lyapunov exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 565-572.
    2. repec:zbw:bofrdp:2006_009 is not listed on IDEAS
    3. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    4. Shintani, Mototsugu, 2008. "A dynamic factor approach to nonlinear stability analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2788-2808, September.
    5. 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.
    6. repec:zbw:bofrdp:2007_020 is not listed on IDEAS
    7. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.
    8. Mikael Bask & Anna Widerberg, 2012. "Actual and potential market risks during the stock market turmoil 2007--2008," Applied Financial Economics, Taylor & Francis Journals, vol. 22(5), pages 339-349, March.
    9. Mototsugu Shintani, 2006. "A nonparametric measure of convergence towards purchasing power parity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 589-604.
    10. 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.
    11. 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.
    12. 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.
    13. Miia Bask & Mikael Bask, 2015. "Cumulative (Dis)Advantage and the Matthew Effect in Life-Course Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.
    14. H. Peter Boswijk & Philip Hans Franses & Dick van Dijk, 2000. "Asymmetric and Common Absorption of Shocks in Nonlinear Autoregressive Models," Econometric Society World Congress 2000 Contributed Papers 0765, Econometric Society.
    15. Bask, Miia & Bask, Mikael, 2014. "Social influence and the Matthew mechanism: The case of an artificial cultural market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 113-119.
    16. Mototsugu Shintani, 2006. "A nonparametric measure of convergence towards purchasing power parity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 589-604, July.
    17. Elena Olmedo & Ricardo Gimeno & Lorenzo Escot & Ruth Mateos, 2007. "Convergencia y Estabilidad de los Tipos de Cambio Europeos: Una Aplicación de Exponentes de Lyapunov," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 44(129), pages 91-108.
    18. van Dijk, Dick & Hans Franses, Philip & Peter Boswijk, H., 2007. "Absorption of shocks in nonlinear autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4206-4226, May.
    19. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    20. Mr. Kangni R Kpodar & Ms. Stefania Fabrizio & Kodjovi M. Eklou, 2019. "Export Competitiveness - Fuel Price Nexus in Developing Countries: Real or False Concern?," IMF Working Papers 2019/025, International Monetary Fund.
    21. Georgios Chortareas & George Kapetanios, 2013. "How Puzzling Is The Ppp Puzzle? An Alternative Half‐Life Measure Of Convergence To Ppp," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(3), pages 435-457, April.
    22. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bsu:wpaper:200603. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tung Liu (email available below). General contact details of provider: https://edirc.repec.org/data/debsuus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.