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2019 | 11 | nr 2 | 107--131
Tytuł artykułu

The Bayesian Methods of Jump Detection: The Example of Gas and EUA Contract Prices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper we present and apply a Bayesian jump-diffusion model and stochastic volatility models with jumps. The problem of how to classify an observation as a result of a jump is addressed, under the Bayesian approach, by introducing latent variables. The empirical study is focused on the time series of gas forward contract prices and EUA futures prices. We analyse the frequency of jumps and relate the moments in which jumps occur to calendar effects or political and economic events and decisions. The calendar effects explain many jumps in gas contract prices. The single jump is identified in the EUA futures prices under the SV-type models. The jump is detected on the day the European Parliament voted against the European Commission's proposal of backloading. The Bayesian results are compared with the outcomes of selected non-Bayesian techniques used for detecting jumps. (original abstract)
Rocznik
Tom
11
Numer
Strony
107--131
Opis fizyczny
Twórcy
  • Cracow University of Economics, Poland
Bibliografia
  • [1] Bernardo J. M. and Smith A. F. (2009). Bayesian theory. John Wiley & Sons.
  • [2] Brooks C. and Prokopczuk M. (2013, apr). The dynamics of commodity prices. Quantitative Finance 13 (4), 527-542.
  • [3] Chib S. and Greenberg E. (1995). Understanding the metropolis-hastings algorithm. The American Statistician 49, 327-335.
  • [4] Chib S., Nardari F. and Shephard N. (2002). Markov chain monte carlo methods for stochastic volatility models. Journal of Econometrics (108), 281-316.
  • [5] Gamerman D. and Lopes H. F. (2006). Markov Chain Monte Carlo. Stochastic Simulation for Bayesian Inference. Chapman & Hall/CRC.
  • [6] Hagfors L. I., Kamperud H. H., Paraschiv F., Prokopczuk M., Sator A. and Westgaard S. (2016). Prediction of extreme price occurrences in the german dayahead electricity market. Quantitative Finance 16 (12), 1929-1948.
  • [7] Jacquier E., Polson N. and Rossi P. (1994). Bayesian analysis of stochastic volatility models. Journal of Business & Economic Statistics 12 (4), 371-389.
  • [8] Jacquier E., Polson N., and Rossi P. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122 (1), 185-212.
  • [9] Janczura J., Trück S., Weron R. and Wolff R. (2013). Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling. Energy Economics 38, 96-110.
  • [10] Johannes M. and Polson N. (2010). MCMC methods for continuous-time financial econometrics. [in:] Handbook of Financial Econometrics: Applications, pp. 1-72. Elsevier.
  • [11] Kass R. and Raftery A. (1995). Bayes factors. Journal of the American Statistical Association 90, 773-795.
  • [12] Kostrzewska J. and Kostrzewski M. (2018). The logistic regression in predicting spike occurrences in electricity prices [in:] The 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena: Conference Proceedings, pp. 219-228. Foundation of the Cracow University of Economics.
  • [13] Kostrzewski M. (2014a). Bayesian inference for the jump-diffusion model with m jumps. Communications in Statistics - Theory and Methods 43, 3955-3985. DOI: 10.1080/03610926.2012.755202.
  • [14] Kostrzewski M. (2014b). Some method of detecting the jump clustering phenomenon in financial time series. [in:] Rusnak Z. and Zmyślona B. (Eds.), 17- th International Scientific Conference Applications of Mathematics and Statistics in Economics, Wrocław, Poland, pp. 141-150. Wrocław University of Economics. DOI: 10.15611/amse.2014.17.15.
  • [15] Kostrzewski M. (2015). Bayesian DEJD model and detection of asymmetry in jump sizes. Central European Journal of Economic Modelling and Econometrics 7 (1), 43-70.
  • [16] Kostrzewski M. (2016). Bayesian SVLEDEJ model for detecting jumps in logarithmic growth rates of one month forward gas contract prices. Central European Journal of Economic Modelling and Econometrics 8 (3), 161-179.
  • [17] Kostrzewski M. and Kostrzewska J. (2019). Probabilistic electricity price forecasting with bayesian stochastic volatility models. Energy Economics 80, 610- 620.
  • [18] Kou S. (2002). A jump-diffusion model for option pricing. Management Science 48, 1086-1101.
  • [19] Kou S. and Wang H. (2004). Option pricing under a double exponential jump diffusion model. Management Science 50 (9), 1178-1192.
  • [20] Lenk P. (2009). Simulation pseudo-bias correction to the harmonic mean estimator of integrated likelihoods. Journal of Computational and Graphical Statistics (18), 941-960.
  • [21] Li H., Wells M., and Yu C. (2008). A Bayesian analysis of return dynamics with Levy jumps. The Review of Financial Studies 21 (5), 2345-2378.
  • [22] Merton R. C. (1976). Option pricing when underlying stock return rates are discontinuous. Journal of Financial Economics 3 (1-2), 125-144.
  • [23] Newton M. A. and Raftery A. E. (1994). Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion). Journal of the Royal Statistical Society B 56 (1), 3-48.
  • [24] Omori Y., Chib S., Shephard N. and Nakajima J. (2007). Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics 140 (2), 425-449.
  • [25] Osiewalski J. and Osiewalski K. (2016). Hybrid MSV-MGARCH models general remarks and the GMSF-SBEKK specification. Central European Journal of Economic Modelling and Econometrics 8 (4), 241-271.
  • [26] Osiewalski K. and Osiewalski J. (2013). A long-run relationship between daily prices on two markets: The bayesian VAR(2)-MSF-SBEKK model. Central European Journal of Economic Modelling and Econometrics 5 (1), 65-83.
  • [27] Pajor A. (2003). Procesy zmienności stochastycznej SV w bayesowskiej analizie finansowych szeregóow czasowych. Monografie: Prace Doktorskie. Akademia Ekonomiczna w Krakowie. (in Polish).
  • [28] Pajor A. (2017). Estimating the marginal likelihood usingthe arithmetic mean identity. Bayesian Analysis 12 (1), 261-287.
  • [29] Pajor A. and Osiewalski J. (2013). A note on Lenk's correction of the harmonic mean estimator. Central European Journal of Economic Modelling and Econometrics 5 (4), 271-275.
  • [30] Pajor A. and Osiewalski J. (2014). Correction to the paper "A note on Lenk's correction of the harmonic mean estimator", Pajor A. and Osiewalski J., Central European Journal of Economic Modelling and Econometrics 5 (2013), 271-275. Central European Journal of Economic Modelling and Econometrics 6 (1), 69-69.
  • [31] Raftery A. E., Newton M. A., Satagopan J. M. and Krivitsky P. N. (2007). Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Bayesian Statistics 8, 1-45.
  • [32] Ramezani C. A. and Zeng Y. (1998, December). Maximum likelihood estimation of asymmetric jump-diffusion models. Working paper http://cyrus.cob. calpoly.edu/JUMPMLE/Ramezani-Zeng-PBJD.pdf.
  • [33] Szerszen P. (2009). Bayesian analysis of stochastic volatility models with Levy jumps: Application to risk analysis. Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C (40), 1-52.
  • [34] Weron R. (2006). Modeling and Forecasting Electricity Loads and Prices. A Statistical Approach. John Wiley & Sons Ltd.
  • [35] Weron R., Bierbrauer M. and Trück S. (2004). Modeling electricity prices: jump diffusion and regime switching. Physica A: Statistical Mechanics and its Applications 336 (1-2), 39-48.
  • [36] Yu B. and Mykland P. (1998). Looking at Markov samplers through cumsum path plots: A simple diagnostic idea. Statistics and Computing 8 (3), 275-286.
  • [37] Yu J. (2005). On leverage in a stochastic volatility model. Journal of Econometrics 127 (2), 165-178.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171561487

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