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Goodness-of-fit testing for the marginal distribution of regime-switching models

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  • Janczura, Joanna
  • Weron, Rafal

Abstract

In this paper we propose a new goodness-of-fit testing scheme for the marginal distribution of regime-switching models. We consider models with an observable (like threshold autoregressions), as well as, a latent state process (like Markov regime-switching). The test is based on the Kolmogorov-Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. The motivation for this research comes from a recent stream of literature in energy economics concerning electricity spot price models. While the existence of distinct regimes in such data is generally unquestionable (due to the supply stack structure), the actual goodness-of-fit of the models requires statistical validation. We illustrate the proposed scheme by testing whether a commonly used Markov regime-switching model fits deseasonalized electricity prices from the NEPOOL (U.S.) day-ahead market.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32532.

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Date of creation: 09 Jul 2011
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Handle: RePEc:pra:mprapa:32532

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Keywords: Regime-switching; marginal distribution; goodness-of-fit; weighted empirical distribution function; Kolmogorov-Smirnov test;

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References

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  1. Marine Carrasco & Liang Hu, 2004. "Optimal test for Markov switching," Econometric Society 2004 North American Summer Meetings, Econometric Society 396, Econometric Society.
  2. Joanna Janczura & Rafal Weron, 2011. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/11/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  3. Bierbrauer, Michael & Menn, Christian & Rachev, Svetlozar T. & Truck, Stefan, 2007. "Spot and derivative pricing in the EEX power market," Journal of Banking & Finance, Elsevier, Elsevier, vol. 31(11), pages 3462-3485, November.
  4. De Jong Cyriel, 2006. "The Nature of Power Spikes: A Regime-Switch Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 10(3), pages 1-28, September.
  5. Rafal Weron & Adam Misiorek, 2005. "Modeling and forecasting electricity loads: A comparison," Econometrics, EconWPA 0502004, EconWPA.
  6. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models or electricity spot prices," MPRA Paper 20546, University Library of Munich, Germany.
  7. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, Econometric Society, vol. 75(6), pages 1671-1720, November.
  8. Karakatsani Nektaria V & Bunn Derek W., 2010. "Fundamental and Behavioural Drivers of Electricity Price Volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 14(4), pages 1-42, September.
  9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  10. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 13(1), pages 1-41, March.
  11. Thomas Lux & Leonardo Morales-Arias, 2009. "Forecasting Volatility under Fractality, Regime-Switching, Long Memory and Student-t Innovations," Kiel Working Papers 1532, Kiel Institute for the World Economy.
  12. Hu Liang & Shin Yongcheol, 2008. "Optimal Test for Markov Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 12(3), pages 1-27, September.
  13. René Garcia, 1995. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," CIRANO Working Papers, CIRANO 95s-07, CIRANO.
  14. Weron, Rafal, 2008. "Heavy-tails and regime-switching in electricity prices," MPRA Paper 10424, University Library of Munich, Germany.
  15. Kim, C-J., 1991. "Dynamic Linear Models with Markov-Switching," Papers, York (Canada) - Department of Economics 91-8, York (Canada) - Department of Economics.
  16. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 39-70.
  17. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601.
  18. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, Springer, vol. 23(4), pages 541-564, October.
  19. John Davis, 2005. "Introduction," Journal of Economic Methodology, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(3), pages 361-361.
  20. Withers, Christopher S. & Nadarajah, Saralees, 2010. "The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions," Statistics & Probability Letters, Elsevier, Elsevier, vol. 80(13-14), pages 1093-1102, July.
  21. Misiorek Adam & Trueck Stefan & Weron Rafal, 2006. "Point and Interval Forecasting of Spot Electricity Prices: Linear vs. Non-Linear Time Series Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, De Gruyter, vol. 10(3), pages 1-36, September.
  22. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, Elsevier, vol. 70(1), pages 127-157, January.
  23. Trueck, Stefan & Weron, Rafal & Wolff, Rodney, 2007. "Outlier Treatment and Robust Approaches for Modeling Electricity Spot Prices," MPRA Paper 4711, University Library of Munich, Germany.
  24. Karakatsani, Nektaria V. & Bunn, Derek W., 2008. "Forecasting electricity prices: The impact of fundamentals and time-varying coefficients," International Journal of Forecasting, Elsevier, Elsevier, vol. 24(4), pages 764-785.
  25. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  26. Jan Bulla & Andreas Berzel, 2008. "Computational issues in parameter estimation for stationary hidden Markov models," Computational Statistics, Springer, Springer, vol. 23(1), pages 1-18, January.
  27. Sen, Rituparna & Hsieh, Fushing, 2009. "A note on testing regime switching assumption based on recurrence times," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(24), pages 2443-2450, December.
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Citations

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Cited by:
  1. Joanna Janczura & Rafał Weron, 2012. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," AStA Advances in Statistical Analysis, Springer, Springer, vol. 96(3), pages 385-407, July.
  2. Weron, Rafal & Janczura, Joanna, 2010. "Efficient estimation of Markov regime-switching models: An application to electricity wholesale market prices," MPRA Paper 26628, University Library of Munich, Germany.
  3. Joanna Janczura, 2012. "Pricing electricity derivatives within a Markov regime-switching model," Papers 1203.5442, arXiv.org.
  4. Joanna Janczura & Rafal Weron, 2012. "Inference for Markov-regime switching models of electricity spot prices," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/12/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  5. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, Elsevier, vol. 32(5), pages 1059-1073, September.
  6. Joanna Janczura, 2014. "Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach," Computational Statistics, Springer, Springer, vol. 79(1), pages 1-30, February.
  7. Xu, Zheng, 2013. "Estimation of parametric homogeneous stochastic volatility pricing formulae based on option data," Economics Letters, Elsevier, Elsevier, vol. 120(3), pages 369-373.

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