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Forecasting Commodity Prices: GARCH, Jumps, and Mean Reversion

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  • Jean-Thomas Bernard
  • Lynda Khalaf
  • Maral Kichian
  • Sebastien McMahon

Abstract

Fluctuations in the prices of various natural resource products are of concern in both policy and business circles; hence, it is important to develop accurate price forecasts. Structural models provide valuable insights into the causes of price movements, but they are not necessarily the best suited for forecasting given the multiplicity of known and unknown factors that affect supply and demand conditions in these markets. Parsimonious representations of price processes often prove more useful for forecasting purposes. Central questions in such stochastic models often revolve around the time-varying trend, the stochastic convenience yield and volatility, and mean reversion. The authors seek to assess and compare alternative approaches to modelling these effects, focusing on forecast performance. Three econometric specifications are considered that cover the most up-to-date models in the recent literature on commodity prices: (i) random-walk models with autoregressive conditional heteroscedasticity (ARCH) or generalized ARCH (GARCH) effects, and with normal or student-t innovations, (ii) Poisson-based jump-diffusion models with ARCH or GARCH effects, and with normal or student-t innovations, and (iii) meanreverting models that allow for uncertainty in equilibrium price.

Suggested Citation

  • Jean-Thomas Bernard & Lynda Khalaf & Maral Kichian & Sebastien McMahon, 2006. "Forecasting Commodity Prices: GARCH, Jumps, and Mean Reversion," Staff Working Papers 06-14, Bank of Canada.
  • Handle: RePEc:bca:bocawp:06-14
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    References listed on IDEAS

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    1. Stacie Beck, 2001. "Autoregressive conditional heteroscedasticity in commodity spot prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(2), pages 115-132.
    2. Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-351, July.
    3. Labys, W. C. & Achouch, A. & Terraza, M., 1999. "Metal prices and the business cycle," Resources Policy, Elsevier, vol. 25(4), pages 229-238, December.
    4. Akgiray, Vedat, et al, 1991. "Conditional Dependence in Precious Metal Prices," The Financial Review, Eastern Finance Association, vol. 26(3), pages 367-386, August.
    5. Saphores, J.D. & Khalaf, L. & Pelletier, D., 2000. "On Jumps and ARCH Effects in Natural Resource Prices. An Application to Stumpage Prices from Pacific Northwest National Forests," Papers 00-03, Laval - Recherche en Energie.
    6. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    7. Khalaf, Lynda & Saphores, Jean-Daniel & Bilodeau, Jean-Francois, 2003. "Simulation-based exact jump tests in models with conditional heteroskedasticity," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 531-553, December.
    8. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    9. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    10. Ahrens, W. Ashley & Sharma, Vijaya R., 1997. "Trends in Natural Resource Commodity Prices: Deterministic or Stochastic?," Journal of Environmental Economics and Management, Elsevier, vol. 33(1), pages 59-74, May.
    11. Winters,L. Alan & Sapsford,David (ed.), 1990. "Primary Commodity Prices," Cambridge Books, Cambridge University Press, number 9780521385503, September.
    12. Gilbert, Christopher L, 1995. "Modelling Market Fundamentals: A Model of the Aluminum Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 385-410, Oct.-Dec..
    13. Robert S. Pindyck, 1999. "The Long-Run Evolutions of Energy Prices," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 1-27.
    14. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    15. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    16. repec:bla:jfinan:v:43:y:1988:i:1:p:155-74 is not listed on IDEAS
    17. Perron, P, 1993. "Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]," Econometrica, Econometric Society, vol. 61(1), pages 248-249, January.
    18. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    19. Drost, Feike C & Nijman, Theo E & Werker, Bas J M, 1998. "Estimation and Testing in Models Containing Both Jump and Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 237-243, April.
    20. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    21. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    22. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    23. Bates, David S., 1996. "Dollar jump fears, 1984-1992: distributional abnormalities implicit in currency futures options," Journal of International Money and Finance, Elsevier, vol. 15(1), pages 65-93, February.
    24. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    25. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    26. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    27. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    28. Jean-Daniel Saphores & Lynda Khalaf & Denis Pelletier, 2002. "On Jumps and ARCH Effects in Natural Resource Prices: An Application to Pacific Northwest Stumpage Prices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(2), pages 387-400.
    29. Akgiray, Vedat & Booth, G Geoffrey, 1988. "Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 631-637, November.
    30. Ball, Clifford A & Torous, Walter N, 1985. "On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
    31. B. Wade Brorsen & Seung-Ryong Yang, 1994. "Nonlinear Dynamics And The Distribution Of Daily Stock Index Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(2), pages 187-203, June.
    32. Labys, W C & Lesourd, J B & Badillo, D, 1998. "The existence of metal price cycles," Resources Policy, Elsevier, vol. 24(3), pages 147-155, September.
    33. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
    34. Moore, Michael J & Cullen, Ursula, 1995. "Speculative Efficiency on the London Metal Exchange," The Manchester School of Economic & Social Studies, University of Manchester, vol. 63(3), pages 235-256, September.
    35. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Keywords

    Econometric and statistical methods;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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