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Parameter instability, stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market

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  • Nonejad, Nima

Abstract

Stochastic volatility models with fixed parameters can be too restrictive for time-series analysis due to instability in the parameters that govern conditional volatility dynamics. We incorporate time-variation in the model parameters for the plain stochastic volatility model as well its extensions with: Leverage, volatility feedback effects and heavy-tailed distributed innovations. With regards to estimation, we rely on one recently discovered result, namely, that when an unbiasedly simulated estimated likelihood (available for example through a particle filter) is used inside a Metropolis-Hastings routine then the estimation error makes no difference to the equilibrium distribution of the algorithm, the posterior distribution. This in turn provides an off-the-shelf technique to estimate complex models. We examine the performance of this technique on simulated and crude oil returns from 1987 to 2016. We find that (i): There is clear evidence of time-variation in the model parameters, (ii): Time-varying parameter volatility models with leverage/Student's t-distributed innovations perform best, (iii): The timing of parameter changes align very well with events such as market turmoils and financial crises.

Suggested Citation

  • Nonejad, Nima, 2017. "Parameter instability, stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market," Economic Modelling, Elsevier, vol. 61(C), pages 388-408.
  • Handle: RePEc:eee:ecmode:v:61:y:2017:i:c:p:388-408
    DOI: 10.1016/j.econmod.2016.11.003
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    as
    1. Arouri, Mohamed El Hédi & Lahiani, Amine & Lévy, Aldo & Nguyen, Duc Khuong, 2012. "Forecasting the conditional volatility of oil spot and futures prices with structural breaks and long memory models," Energy Economics, Elsevier, vol. 34(1), pages 283-293.
    2. Bradley T. Ewing & Farooq Malik, 2010. "Estimating Volatility Persistence in Oil Prices Under Structural Breaks," The Financial Review, Eastern Finance Association, vol. 45(4), pages 1011-1023, November.
    3. Salisu, Afees A. & Fasanya, Ismail O., 2013. "Modelling oil price volatility with structural breaks," Energy Policy, Elsevier, vol. 52(C), pages 554-562.
    4. Bauwens, Luc & Dufays, Arnaud & Rombouts, Jeroen V.K., 2014. "Marginal likelihood for Markov-switching and change-point GARCH models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 508-522.
    5. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 326-360, Summer.
    6. Hung, Jui-Cheng & Lee, Ming-Chih & Liu, Hung-Chun, 2008. "Estimation of value-at-risk for energy commodities via fat-tailed GARCH models," Energy Economics, Elsevier, vol. 30(3), pages 1173-1191, May.
    7. Boyer, M. Martin & Filion, Didier, 2007. "Common and fundamental factors in stock returns of Canadian oil and gas companies," Energy Economics, Elsevier, vol. 29(3), pages 428-453, May.
    8. Narayan, Paresh Kumar & Narayan, Seema, 2007. "Modelling oil price volatility," Energy Policy, Elsevier, vol. 35(12), pages 6549-6553, December.
    9. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    10. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    11. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    12. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
    13. Lardic, Sandrine & Mignon, Valérie, 2008. "Oil prices and economic activity: An asymmetric cointegration approach," Energy Economics, Elsevier, vol. 30(3), pages 847-855, May.
    14. Phan, Dinh Hoang Bach & Sharma, Susan Sunila & Narayan, Paresh Kumar, 2015. "Stock return forecasting: Some new evidence," International Review of Financial Analysis, Elsevier, vol. 40(C), pages 38-51.
    15. He, Zhongfang & Maheu, John M., 2010. "Real time detection of structural breaks in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2628-2640, November.
    16. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    17. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    18. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    19. Hedi Arouri, Mohamed El & Khuong Nguyen, Duc, 2010. "Oil prices, stock markets and portfolio investment: Evidence from sector analysis in Europe over the last decade," Energy Policy, Elsevier, vol. 38(8), pages 4528-4539, August.
    20. Fan, Ying & Zhang, Yue-Jun & Tsai, Hsien-Tang & Wei, Yi-Ming, 2008. "Estimating 'Value at Risk' of crude oil price and its spillover effect using the GED-GARCH approach," Energy Economics, Elsevier, vol. 30(6), pages 3156-3171, November.
    21. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    22. Chris Brooks & Marcel Prokopczuk, 2013. "The dynamics of commodity prices," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 527-542, March.
    23. Alizadeh, Amir H. & Nomikos, Nikos K. & Pouliasis, Panos K., 2008. "A Markov regime switching approach for hedging energy commodities," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1970-1983, September.
    24. Cologni, Alessandro & Manera, Matteo, 2008. "Oil prices, inflation and interest rates in a structural cointegrated VAR model for the G-7 countries," Energy Economics, Elsevier, vol. 30(3), pages 856-888, May.
    25. Vo, Minh T., 2009. "Regime-switching stochastic volatility: Evidence from the crude oil market," Energy Economics, Elsevier, vol. 31(5), pages 779-788, September.
    26. Chang-Jin Kim & Charles R. Nelson, 1998. "Business Cycle Turning Points, A New Coincident Index, And Tests Of Duration Dependence Based On A Dynamic Factor Model With Regime Switching," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 188-201, May.
    27. Fong, Wai Mun & See, Kim Hock, 2002. "A Markov switching model of the conditional volatility of crude oil futures prices," Energy Economics, Elsevier, vol. 24(1), pages 71-95, January.
    28. Narayan, Paresh Kumar & Narayan, Seema & Sharma, Susan Sunila, 2013. "An analysis of commodity markets: What gain for investors?," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3878-3889.
    29. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(05), pages 933-956, October.
    30. Kang, Sang Hoon & Cheong, Chongcheul & Yoon, Seong-Min, 2011. "Structural changes and volatility transmission in crude oil markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4317-4324.
    31. Perry Sadorsky, 2005. "Stochastic volatility forecasting and risk management," Applied Financial Economics, Taylor & Francis Journals, vol. 15(2), pages 121-135.
    32. Oberndorfer, Ulrich, 2009. "Energy prices, volatility, and the stock market: Evidence from the Eurozone," Energy Policy, Elsevier, vol. 37(12), pages 5787-5795, December.
    33. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    34. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    35. Larsson, Karl & Nossman, Marcus, 2011. "Jumps and stochastic volatility in oil prices: Time series evidence," Energy Economics, Elsevier, vol. 33(3), pages 504-514, May.
    36. Bina Cyrus & Vo Minh, 2007. "OPEC in the Epoch of Globalization: An Event Study of Global Oil Prices," Global Economy Journal, De Gruyter, vol. 7(1), pages 1-52, February.
    37. Wai Mun Fong & Kim Hock See, 2003. "Basis variations and regime shifts in the oil futures market," The European Journal of Finance, Taylor & Francis Journals, vol. 9(5), pages 499-513.
    38. Paresh Kumar Narayan & Stephan Popp, 2010. "A new unit root test with two structural breaks in level and slope at unknown time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1425-1438.
    39. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    40. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
    41. Narayan, Paresh Kumar & Sharma, Susan & Poon, Wai Ching & Westerlund, Joakim, 2014. "Do oil prices predict economic growth? New global evidence," Energy Economics, Elsevier, vol. 41(C), pages 137-146.
    42. Hamilton, James D, 1983. "Oil and the Macroeconomy since World War II," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 228-248, April.
    43. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    44. Narayan, Paresh Kumar & Liu, Ruipeng, 2015. "A unit root model for trending time-series energy variables," Energy Economics, Elsevier, vol. 50(C), pages 391-402.
    45. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    46. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    47. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    48. Aloui, Chaker & Jammazi, Rania, 2009. "The effects of crude oil shocks on stock market shifts behaviour: A regime switching approach," Energy Economics, Elsevier, vol. 31(5), pages 789-799, September.
    49. Agnolucci, Paolo, 2009. "Volatility in crude oil futures: A comparison of the predictive ability of GARCH and implied volatility models," Energy Economics, Elsevier, vol. 31(2), pages 316-321, March.
    50. Narayan, Paresh Kumar & Sharma, Susan Sunila, 2015. "Does data frequency matter for the impact of forward premium on spot exchange rate?," International Review of Financial Analysis, Elsevier, vol. 39(C), pages 45-53.
    51. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Modeling energy price dynamics: GARCH versus stochastic volatility," Energy Economics, Elsevier, vol. 54(C), pages 182-189.
    52. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    53. Nandha, Mohan & Faff, Robert, 2008. "Does oil move equity prices? A global view," Energy Economics, Elsevier, vol. 30(3), pages 986-997, May.
    54. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    55. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    56. Cathy W. S. Chen & Mike K. P. So & Ming-Tien Chen, 2005. "A Bayesian threshold nonlinearity test for financial time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(1), pages 61-75.
    57. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    58. Jones, Charles M & Kaul, Gautam, 1996. " Oil and the Stock Markets," Journal of Finance, American Finance Association, vol. 51(2), pages 463-491, June.
    59. Berry Wilson & Reena Aggarwal & Carla Inclan, 1996. "Detecting volatility changes across the oil sector," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(3), pages 313-330, May.
    60. Nomikos, Nikos K. & Pouliasis, Panos K., 2011. "Forecasting petroleum futures markets volatility: The role of regimes and market conditions," Energy Economics, Elsevier, vol. 33(2), pages 321-337, March.
    61. Joshua C. C. Chan & Angelia L. Grant, 2016. "On the Observed-Data Deviance Information Criterion for Volatility Modeling," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(4), pages 772-802.
    62. Narayan, Paresh Kumar & Sharma, Susan Sunila, 2011. "New evidence on oil price and firm returns," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3253-3262.
    63. Malik, S. & Pitt, M. K., 2011. "Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering," Working papers 318, Banque de France.
    64. Ciner Cetin, 2001. "Energy Shocks and Financial Markets: Nonlinear Linkages," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(3), pages 1-11, October.
    65. Kang, Sang Hoon & Kang, Sang-Mok & Yoon, Seong-Min, 2009. "Forecasting volatility of crude oil markets," Energy Economics, Elsevier, vol. 31(1), pages 119-125, January.
    66. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Keywords

    Bayes; Crude oil; Metropolis-Hastings; Parameter instability; Particle filtering;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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