Janczura, Joanna and Weron, Rafal (2012): Goodnessoffit testing for the marginal distribution of regimeswitching models.
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Abstract
In this paper we propose a new goodnessoffit testing scheme for the marginal distribution of regimeswitching models. We consider models with an observable (like threshold autoregressions), as well as, a latent state process (like Markov regimeswitching). The test is based on the KolmogorovSmirnov supremumdistance 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 goodnessoffit of the models requires statistical validation. We illustrate the proposed scheme by testing whether commonly used Markov regimeswitching models fit deseasonalized electricity prices from the NEPOOL (U.S.) dayahead market.
Item Type:  MPRA Paper 

Original Title:  Goodnessoffit testing for the marginal distribution of regimeswitching models 
Language:  English 
Keywords:  Regimeswitching; marginal distribution; goodnessoffit; weighted empirical distribution function; KolmogorovSmirnov test; conditional independence 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General Q  Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q4  Energy 
Item ID:  36461 
Depositing User:  Rafal Weron 
Date Deposited:  06 Feb 2012 12:18 
Last Modified:  27 Apr 2016 16:49 
References:  Bally, V., Talay, D., (1996) The law of the Euler scheme for stochastic differential equations: II. Convergence rate of the density. Monte Carlo Methods and Applications 2, 93128. Bierbrauer, M., Menn, C., Rachev, S.T., Trueck, S. (2007). Spot and derivative pricing in the EEX power market. Journal of Banking and Finance 31, 34623485. Billingsley, P. (1968) Convergence of Probability Measures, Wiley, New York. Billingsley, P. (1986) Probability and Measure (2nd ed.), Wiley, New York. Brockwell, P.J., Davis, R.A. (1996) Introduction to Time Series and Forecasting (2nd ed.), SpringerVerlag, New York. Bulla, J., Berzel, A. (2008) Computational issues in parameter estimation for stationary hidden Markov models. Computational Statistics 23: 118. Cappe, O., Moulines E., Ryden T. (2005) Inference in Hidden Markov Models. Springer. Celeux, G., Durand, J.B. (2008) Selecting hidden Markov model state number with crossvalidated likelihood. Computational Statistics 23, 541564. Cetin, M., Comert, G. (2006) Shortterm traffic flow prediction with regime switching models. Transportation Research Record: Journal of the Transportation Research Board 1965, 2331. Cho, J.S., White, H. (2007) Testing for regime switching. Econometrica 75(6), 16711720. Choi, S. (2009) Regimeswitching univariate diffusion models of the shortterm interest rate. Studies in Nonlinear Dynamics & Econometrics 13(1), Article 4. Cizek P, Haerdle W, Weron R, eds. (2011) Statistical Tools for Finance and Insurance (2nd ed.). Springer, Berlin. Cox, J.C., Ingersoll, J.E., Ross, S.A. (1985). A theory of the term structure of interest rates. Econometrica 53, 385407. D’Agostino R.B., Stevens M.A., eds. (1986) Goodnessoffit testing techniques. Marcel Dekker, New York. De Jong, C. (2006). The nature of power spikes: A regimeswitch approach. Studies in Nonlinear Dynamics & Econometrics 10(3), Article 3. Ethier, R., Mount, T., (1998). Estimating the volatility of spot prices in restructured electricity markets and the implications for option values. PSerc Working Paper 9831. Eydeland, A., Wolyniec, K. (2012) Energy and Power Risk Management (2nd ed.). Wiley, Hoboken, NJ. Garcia, R. (1998) Asymptotic null distribution of the likelihood ratio test in Markov switching models. International Economic Review 39, 763788. Grzenda, W., Zieba, W. (2008) Conditional Central Limit Theorem. International Mathematical Forum 3(31), 15211528. Haeusler, E., Mason, D.M., Newton, M.A. (1991) Weighted bootstrapping of the means. CWI Quaterly, 213228. Hamilton, J. (1990) Analysis of time series subject to changes in regime. Journal of Econometrics 45, 3970. Hamilton, J. (1996) Specification testing in Markovswitching time series models. Journal of Econometrics 70, 127157. Hamilton, J. (1996) Regime switching models. In: The New Palgrave Dictionary of Economics (2nd ed.). Hirsch, G. (2009) Pricing of hourly exercisable electricity swing options using different price processes. Journal of Energy Markets 2(2), 346. Hu, L., Shin, Y. (2008) Optimal test for Markov switching GARCH models. Studies in Nonlinear Dynamics & Econometrics 12(3), Article 3. Huang, M.L., Brill, P.H. (2004) A distribution estimation method based on level crossings. Journal of Statistical Planning and Inference 124, 4562. Huisman, R., de Jong, C. (2003). Option pricing for power prices with spikes. Energy Power Risk Management 7.11, 1216. Janczura, J., Weron, R. (2009) Regime switching models for electricity spot prices: Introducing heteroskedastic base regime dynamics and shifted spike distributions. IEEE Con ference Proceedings (EEM’09), DOI 10.1109/EEM.2009.5207175. Available at MPRA: http://mpra.ub.unimuenchen.de/18784. Janczura, J., Weron, R. (2010) An empirical comparison of alternate regimeswitching models for electricity spot prices. Energy Economics 32(5), 10591073. Janczura, J., Weron, R. (2012) Efficient estimation of Markov regimeswitching models: An application to electricity wholesale market prices. AStA – Advances in Statistical Analysis, Online First doi:10.1007/s1018201101812. Karakatsani, N.V., Bunn, D. (2008) Forecasting electricity prices: The impact of fundamentals and timevarying coefficients. International Journal of Forecasting 24, 764785. Karakatsani, N.V., Bunn, D. (2010) Fundamental and behavioural drivers of electricity price volatility. Studies in Nonlinear Dynamics & Econometrics 14(4), Article 4. Kim, C.J. (1994) Dynamic linear models with Markovswitching. Journal of Econometrics 60, 122. Knittel, C.R., Roberts, M.R. (2005) An empirical examination of restructured electricity prices. Energy Economics 27, 791817. Lehmann, E.L., Romano, J.P. (2005) Testing Statistical Hypotheses (3rd ed.) Springer, New York. Luo, Q., Mao, X. (2007) Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications, 334(1), 6984. Lux, T., MoralesArias, L. (2010) Forecasting volatility under fractality, regimeswitching, long memory and studentt innovations. Computational Statistics and Data Analysis 54, 26762692. Maiboroda, R.E. (1996) Estimates for distributions of components of mixtures with varying concentrations. Ukrainian Mathematical Journal 48(4), 618622. Maiboroda, R.E. (2000) A test for the homogeneity of mixtures with varying concentrations. Ukrainian Mathematical Journal 52(8), 12561263. Mari, C. (2008). Random movements of power prices in competitive markets: A hybrid model approach. Journal of Energy Markets 1(2), 87103. Misiorek, A., Trueck S., Weron R. (2006) Point and interval forecasting of spot electricity prices: linear vs. nonlinear time series models. Studies in Nonlinear Dynamics & Econometrics 10(3), Article 2. Prakasa Rao, B.L.S. (2009) Conditional independence, conditional mixing and conditional association. Annals of the Institute of Statistical Mathematics 61, 441460. Ross, S. (2002) Simulation. Academic Press, San Diego. Sen, R., Hsieh, F. (2009) A note on testing regime switching assumption based on recurrence times. Statistics and Probability Letters 79, 24432450. Trueck, S., Weron, R., Wolff, R. (2007) Outlier treatment and robust approaches for modeling electricity spot prices. Proceedings of the 56th Session of the ISI. Available at MPRA: http://mpra.ub.unimuenchen.de/4711/. Vasas, K., Eleka, P., Markusa, L. (2007) A twostate regime switching autoregressive model with an application to river flow analysis. Journal of Statistical Planning and Inference, 137(10), 31133126. Weron, R. (2006) Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach. Wiley, Chichester. Weron, R. (2009) Heavytails and regimeswitching in electricity prices. Mathematical Methods of Operations Research 69(3), 457473. Withers, C.S., Nadarajah, S. (2010) The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions. arXiv:1002.4338v1. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/36461 
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