GARCH-Type Processes in Modeling Energy Prices

  • Irina Khindanova
  • Zauresh Atakhanova
  • Svetlozar Rachev


High price volatility is a long-standing characteristic of world oil markets and, more recently, of natural gas and electricity markets. However, there is no widely accepted answer to what the best models and measures of price volatility are because of the complexity of distribution of energy prices. Complex distribution patterns and volatility clustering of energy prices have motivated considerable research in energy finance. Such studies propose dealing with the non-normality of energy prices by incorporating models of time-varying conditional volatility or using stochastic models. Several GARCH models have been developed and successfully applied to modeling energy prices. They represent a significant improvement over models of unconditionally normally distributed energy returns. However, such models may be further improved by incorporating the Pareto stable distributed error term. The article compares the performance of normal GARCH models with the statistical properties of unconditional distribution models of energy returns. We then present the results of estimation of energy GARCH based on the stable distributed error term and compare the performance of normal GARCH and stable GARCH.


Energy Price GARCH Model Energy Return Spot Prex Convenience Yield 
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  1. [1]
    Abosedra, S.S. and N.T. Laopodis, 1997, Stochastic Behavior of Crude Oil Prices. A GARCH Investigation, The Journal of Energy and Development, 21(2): 283–291.Google Scholar
  2. [2]
    Adrangi, B., A. Chatrah, K. Raffiee, R.D. Ripple, 2001a, Alaska North Slope Crude Oil Price and the Behavior of Diesel Prices in California, Energy Economics, 23:29–42.Google Scholar
  3. [3]
    Adrangi, B., A. Chatrah, K.K. Dhanda, K. Raffiee, 2001b, Chaos in Oil prices? Evidence from Futures Markets, Energy Economics, 23:405–425.Google Scholar
  4. [4]
    Antoniou, A. and A.J. Foster, 1992, The Effect of Futures Trading on Spot Price Volatility: Evidence for Brent Crude Oil Using GARCH, Journal of Business Finance and Accounting, 19(4): 473–484.Google Scholar
  5. [5]
    Bollerslev, T., 1986, Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31:307–327.Google Scholar
  6. [6]
    Bollerslev, T., 1987, A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of return, Review of Economics and Statistics, 69(3):542–547.Google Scholar
  7. [7]
    Bollerslev, T. and R.F. Engle, D.B. Nelson, 1993, ARCH Models, UCSD Discussion Paper 93-49, November 1993.Google Scholar
  8. [8]
    Boyd, R. and T. Caporale, 1996, Scarcity, Resource Price Uncertainty, and Economic Growth, Land Economics, 72(3):326–335.Google Scholar
  9. [9]
    Brunetti, C. and C.L. Gilbert, 2000, Bivariate FIGARCH and Fractional Cointegration, Journal of Empirical Finance, 7:509–530.Google Scholar
  10. [10]
    Deaves, R. and I. Krinsky, 1992, Risk Premiums and Efficiency in the Market for Crude Oil Futures, The Energy Journal, 13(2):93–117.Google Scholar
  11. [11]
    Dickey, D.A. and W.A. Fuller, 1979, Distribution of the Estimators of Autoregressive Time Series with a Unit Root, Journal of American Statistical Association, 74:472–431.Google Scholar
  12. [12]
    DuMouchel, W., 1973a, Stable Distributions in Statistical Inference: 1. Symmetric Stable Distribution Compared to Other Symmetric Long-Tailed Distributions, Journal of American Statistical Association, 68:469–477.Google Scholar
  13. [13]
    DuMouchel, 1973b, On the Asymptotic Normality of the Maximum Likelihood Estimate when Sampling from a Stable Distribution, Annals of Statistics, 3:948–957.Google Scholar
  14. [14]
    Engle, R.F, 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of the United Kingdom Inflation, Econometrica, 50:276–287.Google Scholar
  15. [15]
    Engle, R. F and T. Bollerslev, 1986, Modelling Persistence of Conditional Variances, Econometric Reviews, 5:1–50.Google Scholar
  16. [16]
    Hamilton, J.D., 1994, Time Series Analysis, Princeton University Press.Google Scholar
  17. [17]
    Khindanova, I. and Z. Atakhanova, 2002, Stable Modeling in Energy Risk Management, Mathematical Methods of Operations Research, 55(2): 225–245.Google Scholar
  18. [18]
    Kwiatkowski, D., C.B. Phillips, P. Schmidt, Y. Shin, 1992, Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root, Journal of Econometrics, 54:159–178.Google Scholar
  19. [19]
    Liu, S.-M. and B.W. Brorsen, 1995, Maximum Likelihood Estimation of a Garch-Stable Model, Journal of Applied Econometrics, 10(3):273–285.Google Scholar
  20. [20]
    Mazaheri, A., 1999, Convenience Yield, Mean Reverting Prices, and Long Memory in the Petroleum Market, Applied Financial Economics, 9:31–50.Google Scholar
  21. [21]
    McKinnon, J., 1991, Critical Values for Cointegration Tests, in: Long-run Economic Relationships, R.F. Engle and C.W.J. Granger, eds., Oxford University Press, London, pp. 267–276Google Scholar
  22. [22]
    Mittnik, S., T. Doganoglu, D. Chenyao, 1999, Computing the Probability Density Function of the Stable Paretian Distribution, Mathematical and Computer Modelling, 29:235–240.Google Scholar
  23. [23]
    Mittnik, S., S.T. Rachev, T. Doganoglu, D. Chenyao, 1999, Maximum Likelihood Estimation of Stable Paretian Models, Mathematical and Computer Modelling, 29:275–293.Google Scholar
  24. [24]
    Moosa, I.A. and N.E. Al-Loughani, 1994, Unbiasedness and Time Varying Risk Premia in the Crude Oil Futures Market, Energy Economics, 16(4):99–105.Google Scholar
  25. [25]
    Morana, C, 2001, A Semiparametric Approach to Short-term Oil Price Forecasting, Energy Economics, 23:325–338.Google Scholar
  26. [26]
    Nelson, D.B., 1990, Stationarity and Persistence in the GARCH (1,1) Model, Econometric Theory, 6:318–334.Google Scholar
  27. [27]
    Nelson, D.B., 1991, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59:229–235.Google Scholar
  28. [28]
    Ng, V.K. and S.C. Pirrong, 1996, Price Dynamics in Refined Petroleum Spot and Futures Markets, Journal of Empirical Finance, 2:359–388.Google Scholar
  29. [29]
    Phillips, P.C.B. and P. Perron, 1988, Testing for a Unit-Root in Time Series Regression, Biometrika, 75:335–346.Google Scholar
  30. [30]
    Rachev, S. and S. Mittnik, 2000, Stable Paretian Models in Finance, John Wiley and Sons Ltd., 1–24.Google Scholar
  31. [31]
    Robinson, T.A. and M.P. Taylor, 1998, Regulatory Uncertainty and the Volatility of Regional Electricity Company Share Prices: The Economic Consequences of Professor Littlechild, Bulletin of Economic Research, 50(1): 37–46.Google Scholar
  32. [32]
    Schwert, G.W., 1989, Why Does Stock Market Volatility Change Over Time?, Journal of Finance, 44:1115–1153.Google Scholar
  33. [33]
    Susmel, R. and A. Thompson, 1997, Volatility, Storage and Convenience: Evidence from Natural Gas Markets, The Journal of Futures Markets, 1997, 17(1): 17–43.Google Scholar
  34. [34]
    Taylor, S., 1986, Modeling Financial Time Series, Wiley and Sons, New York, NY.Google Scholar
  35. [35]
    Wickham, P., 1996, Volatility of Oil Prices, IMF Working Paper WP/96/82.Google Scholar
  36. [36]
    Zolotarev, V.M., 1966, On Representation of the Stable Laws by Integrals, in Selected Translations in Mathematical Statistics and Probability, American Mathematical Society, Providence, RI, 6, 84–88.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Irina Khindanova
    • 1
  • Zauresh Atakhanova
    • 2
  • Svetlozar Rachev
    • 3
    • 4
  1. 1.Colorado School of MinesGoldenUSA
  2. 2.Economics and Strategic Research (KIMEP)Kazakhstan Institute of ManagementAlmaty
  3. 3.Institut für Statistik und Mathematische WirtschaftstheorieUniversität KarlsruheKarlsruheGermany
  4. 4.Department of Statistics and Applied ProbabilityUniversity of CaliforniaSanta BarbaraUSA

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