State Space Model of Brent Oil Price Dynamics
The constant concern in commodities market, particularly in oil price, has necessitated accurate models to aid in the generation of relatively good synthetic oil price data. Oil prices are subject to high volatility and its impact on economic growth has continued to generate controversies among economic researchers and policymakers. In this paper, a state space model approach was developed to describe the dynamics of Brent crude oil prices. The dynamics were examined as a continuous time stochastic process generalized as an Ornstein-Uhlenbeck equation. The result revealed that the dynamic behaviour of Brent oil price is an Ornstein-Uhlenbeck equation depicting a mean reversion process in crude oil prices. The process is stationary Gauss-Markov process and is the only nontrivial process that satisfies the conditions of allowing linear transformations of the space and time variables. The Ornstein-Uhlenbeck process in this paper is considered as the continuous time analogue of the discrete-time autoregressive process of order one (AR(1)).
Gahler, S. 2-Metrische Raume und ihre topologische Struktur. Mathematishe Nachrichten, 26, 115--148, (1963).
Akaike, H. Autoregressive model fitting for the control. Ann. Inst. Statist. Math., 23, 163--180, (1971).
Akaike, H. A New Look at statistical model identification. I.E.E.E. Transactions, (1974).
Barsky, R.B. & Kilian, L. Oil and the Macroeconomy since the 1970s. Journal of Economic Perspectives, 18, 115-134, (2004).
Benard, J., Khalaf, L., Kichian, M., & McMahon, S. Oil Prices: Heavy Tails, Mean Reversion and the Convenience Yield. Working Paper, University of Laval and Bank of Canada. 18, 115-134, (2008).
Box, G.E.P. & Jenkins, G.M . Time series analysis, forecasting and control. (rev.ed), San Franscisco, Holden-Day, 18, 115-134
Bollerslev, T. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307-327, (1986).
Brennan, M. & Schwartz, E. Evaluating Natural Resource Investments. The Journal of Business, 58, 135-157, (1985).
Chatfield, C. The Analysis of Times Series An Introduction, 6th ed , Chapman and Hall/CRC,Boca Raton, (2004).
Chung, K.L and Williams, R. J. Introduction to Stochastic Integration, 2nd edition, Birkhauser, Basel, (1990).
Dafas, P. A. Estimating the parameters of a mean-reverting Markov-switching jump-diffusion model for crude oil spot prices. 25 -- 34, (2004) .
Durbin, J.,& S.J. Koopman . Time Series Analysis of Non-Gaussian Observations based on State-Space Models from Both Classical and Bayesian Perspectives (with discussion). Journal of Royal Statistical Society, Series B, 62, 3-56, (2000).
Durbin, J.& S. J. Koopman . Time series analysis by state space methods. Oxford University Press, Oxford. (2001).
Engle R.F. . Autoregressive Conditional Heteroscedasticity with estimates of the variance of UK inflation. Econometrica, 50, 987-1008, (1982).
Franke, J., Hardle, W.& Hafner, C. Statistics of Financial Markets: An introduction, Springer-Verlag, New York, (2004) .
Geman, H. Mean Reversion versions random walk in Oil and Natural Gas Prices. University of London, United Kingdom, (2007).
Hamilton, J. D. Understanding Crude Oil Prices. Energy Journal, 30, pp 179-206, (2008).
Hamilton, J. D. Causes and Consequences of the Oil Shock of 2007-08. Brookings paper on Economic Activity (Spring), 215--261, (2009).
Harvey, A.C. Forecasting, Structural Time Series Models and Kalman Filter. Cambridge University Press, Cambridge, (1989).
Hotelling, H. The Economics of Exhaustible Resources. Journal of Political Economy, 39, 137-175, (1931).
Huntington, H. G. Oil Shocks and Real U.S. Income. The Energy Journal, 28(4), 31-46, (2007).
Jiménez-Rodríguez, R.& Sánchez, M. Oil price shocks and real GDP growth: empirical evidence from some OECD countries. Applied Economics,
, 201-228, (2005).
Kalman, R.E. A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering Transactions Series D.
, 35-45, (1960).
Laming D.R.J. Information Theory of Choice Reaction Time, Wiley, New York. (1968).
Kosobud, R. F. and Stokes, H. H. Oil Market Share Dynamics: A Markov Chain Analysis of Consumer and Producer Adjustments, Empirical Economics, 3 (4), pp. 253 - 275. (1978)
Lipsky, J, Economic Shifts and Oil Price Volatility. http:// www.imf.org /np speeches/ 2009/031809.htm (2009).
Langevin, P. The theory of Brownian movement. Comp. Rend. 146, 530-532, 1908
Lin, A . Prediction of International Crude oil futures price based on GM(1,1) In Link And Heath, 1975 A Sequential Theory Of Psychological Discrimination Psychometrika, 40 (1975), Pp. 77-105. (2009)
Mikosch,T. Elementary Stochastic Calculus With Finance in View, Advanced Series on Statistical Science and Applied Probability,World Scientific, New Jersey. (2008)
Schwartz, E.S. The Stochastic Behaviour of commodity prices implication for valuation and Hedging. The Journal of finance,
vol 52(3) PP 923-973. (1997)
Taylor, J. and van Doren, P. The Energy Security Obsession, Georgetown Journal of Law and Public Policy, 6(2). (2008)
Tuo, J, and Yanbing. Summary of World Oil Price Forecasting Model, In IEEE Knowledge Acquisition and Modelling (KAM). Fourth International Symposium, pp 327-330. (2011)