Forecasting hourly WTI oil front monthly price volatility densities

Per B. Solibakke; Per B. Solibakke

doi:10.3934/QFE.2024018

Quantitative Finance and Economics

2024, Volume 8, Issue 3: 466-501. doi: 10.3934/QFE.2024018

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Research article

Forecasting hourly WTI oil front monthly price volatility densities

Per B. Solibakke ^,

Faculty of Economics, Norwegian University of Science and Technology, Trondheim, Norway

Received: 05 April 2024 Revised: 12 June 2024 Accepted: 27 June 2024 Published: 08 July 2024
JEL Codes: C61, Q4

Financial commodity markets have an impact on company values and cash flows, where price movements within frequent time intervals can be both significant and random. Understanding highly frequent price movements is both important and difficult. In this paper, I measured and forecasted volatility for high-frequency (mostly twelve hours per day) WTI Oil front month price movements from 2012 to 2024 (about 40,500 observations). I created a new stochastic volatility model for extracting latent volatility using the non-linear Kalman filter. Stable and strictly ergodic hourly price series, along with the BIC optimal non-linear (generic) general method of moments model coefficients, enabled this process. The latent volatility seemed to separate into two volatility factors. One factor that was very persistent suggested slow mean reversion, and one choppy strongly mean-reverting factor. The data dependence found in the factor volatility series suggested forecasting ability. I applied classical static forecasts and three machine learning regression techniques to predict one-step-ahead volatility. The two volatility factors and one summarizing exponential factor were reported, along with several fit measures, including the root mean square error and Theil's measure of covariance.
- data dependency,
- high frequency,
- stochastic volatility,
- international WTI oil prices
Citation: Per B. Solibakke. Forecasting hourly WTI oil front monthly price volatility densities[J]. Quantitative Finance and Economics, 2024, 8(3): 466-501. doi: 10.3934/QFE.2024018

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Abstract

Financial commodity markets have an impact on company values and cash flows, where price movements within frequent time intervals can be both significant and random. Understanding highly frequent price movements is both important and difficult. In this paper, I measured and forecasted volatility for high-frequency (mostly twelve hours per day) WTI Oil front month price movements from 2012 to 2024 (about 40,500 observations). I created a new stochastic volatility model for extracting latent volatility using the non-linear Kalman filter. Stable and strictly ergodic hourly price series, along with the BIC optimal non-linear (generic) general method of moments model coefficients, enabled this process. The latent volatility seemed to separate into two volatility factors. One factor that was very persistent suggested slow mean reversion, and one choppy strongly mean-reverting factor. The data dependence found in the factor volatility series suggested forecasting ability. I applied classical static forecasts and three machine learning regression techniques to predict one-step-ahead volatility. The two volatility factors and one summarizing exponential factor were reported, along with several fit measures, including the root mean square error and Theil's measure of covariance.

References

[1]	Andersen TG (1994) Stochastic autoregressive volatility: a framework for volatility modelling. Math Financ 4: 75–102. https://doi.org/10.1111/j.1467-9965.1994.tb00063.x doi: 10.1111/j.1467-9965.1994.tb00063.x
[2]	Andersen TG, Benzoni L, Lund J (2002) Towards an empirical foundation for continuous-time models. J Financ 57: 1239–1284. https://doi.org/10.1111/1540-6261.00460 doi: 10.1111/1540-6261.00460
[3]	Brock WA, Dechert WD, Scheinkman JA, et al. (1996) A test for independence based on the correlation dimension. Econom Rev 15: 197–235. https://doi.org/10.1080/07474939608800353 doi: 10.1080/07474939608800353
[4]	Black F (1976) Studies of Stock Market Volatility Changes, Proceedings of the American Statistical Association, Business and Economics Section, 177–181.
[5]	Bollerslev T (1986) Generalised Autoregressive Conditional Heteroscedasticity. J Econom 31: 307–27. https://doi.org/10.1016/0304-4076(86)90063-1 doi: 10.1016/0304-4076(86)90063-1
[6]	Bollerslev T (1987) A Conditionally heteroscedastic Time Series Model for Speculative Prices and Rates of Return. Rev Econ Stat 64: 542–547. https://doi.org/10.2307/1925546 doi: 10.2307/1925546
[7]	Bollerslev T, Chou RY, Kroner KF (1992) ARCH modeling in finance. A review of the theory and empirical evidence. J Econom 52: 5–59. https://doi.org/10.1016/0304-4076(92)90064-X doi: 10.1016/0304-4076(92)90064-X
[8]	Box GEP, Jenkins GM (1976) Time Series Analysis: Forecasting and Control, Revised Edition, San Francisco: Holden Day.
[9]	Brock WA, Deckert WD (1988) Theorems on Distinguishing Deterministic from Random Systems, In: Barnett, W.A., Berndt, E.R., White, H., Dynamic Econometric Modelling, Cambridge University Press, 247–268.
[10]	Brock WA, Dechert WD, Scheinkman JA, et al. (1996) A test for independence based on the correlation dimension. Econom Rev 15: 197–235. https://doi.org/10.1080/07474939608800353 doi: 10.1080/07474939608800353
[11]	Campbell JY, Grossman SJ, Wang J (1993) Trading Volume and Serial Correlation in Stock Returns. Q J Econ 108: 905–939. https://doi.org/10.2307/2118454 doi: 10.2307/2118454
[12]	Campbell J, Mankiw NG (1987) Are output fluctuations transitory?. Q J Econ 102: 875–880. https://doi.org/10.2307/1884285 doi: 10.2307/1884285
[13]	Chan KF, Gray P (2006) Using Extreme Value Theory to Measure Value-at-Risk for Daily Electricity Prices. Int J Forecast 22. https://doi.org/10.1016/j.ijforecast.2005.11.005 doi: 10.1016/j.ijforecast.2005.11.005
[14]	Chernov M, Gallant AR, Ghysel E, et al. (2003) Alternative models for stock price dynamics. J Econom 56: 225–257. https://doi.org/10.1016/S0304-4076(02)00202-5 doi: 10.1016/S0304-4076(02)00202-5
[15]	Christie A (1982) The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects. J Financ Econ 10: 407–432. https://doi.org/10.1016/0304-405X(82)90018-6 doi: 10.1016/0304-405X(82)90018-6
[16]	Clark PK (1973) A subordinated stochastic Process model with finite variance for specula-tive prices. Econometrica 41: 135–156. https://doi.org/10.2307/1913889 doi: 10.2307/1913889
[17]	de Lima PJF (1995a) Nonlinearities and Nonstationarities in stock returns. Working Paper in Economics, The Johns Hopkins University, Department of Economics.
[18]	de Lima PJF (1995b) Nuisance parameter free properties of correlation integral based statistics. Econom Rev 15: 237–259. https://doi.org/10.1080/07474939608800354 doi: 10.1080/07474939608800354
[19]	deVany AS, Wall WD (1999) Cointegration analysis of spot electricity prices: insights on transmission efficiency in the western US. Energy Econ 21: 435–448. https://doi.org/10.1016/S0140-9883(99)00011-0 doi: 10.1016/S0140-9883(99)00011-0
[20]	Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74: 427–431. https://doi.org/10.2307/2286348 doi: 10.2307/2286348
[21]	Ding Z, Engle RF, Granger CWJ (1993) A Long memory Property of Stock Market Returns and a New Model. J Empir Financ 1: 83–106. https://doi.org/10.1016/0927-5398(93)90006-D doi: 10.1016/0927-5398(93)90006-D
[22]	Doan T, Litterman R, Sims C (1984) Forecasting and Conditional Projection using Realistic Prior Distributions. Econom Rev 3: 1–100. https://doi.org/10.1080/07474938408800053 doi: 10.1080/07474938408800053
[23]	Durham G (2003) Likelihood-based specification analysis of continuous-time models of the short-term interest rate. J Financ Econ 70: 463–487. https://doi.org/10.1016/S0304-405X(03)00105-7 doi: 10.1016/S0304-405X(03)00105-7
[24]	Engle RF (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation. Econometrica 50: 987–1008. https://doi.org/10.1080/16843703.2004.11673078 doi: 10.1080/16843703.2004.11673078
[25]	Engle RF, Bollerslev T (1986) Modelling the Persistence of Conditional Variances. Econom Rev 5: 1–50. https://doi.org/10.1080/07474938608800095 doi: 10.1080/07474938608800095
[26]	Engle RF, Ng VK (1993) Measuring and Testing the Impact of News on Volatility. J Financ 48: 1749–1778. https://doi.org/10.1111/j.1540-6261.1993.tb05127.x doi: 10.1111/j.1540-6261.1993.tb05127.x
[27]	Engle RF, Patton AJ (2001) What Good is a Volatility Model. Available from: http://archive.nyu.edu/bitstream/2451/26881/2/S-DRP-01-03.pdf.
[28]	Gallant AR, Nychka DW (1987) Semi nonparametric maximum likelihood estimation. Econometrica 55: 363–390. https://doi.org/10.2307/1913241 doi: 10.2307/1913241
[29]	Gallant AR, Rossi PE, Tauchen G (1992) Stock Prices and Volume. Rev Financ Stud 5: 199–242. https://doi.org/10.1093/rfs/5.2.199 doi: 10.1093/rfs/5.2.199
[30]	Gallant AR, Rossi PE, Tauchen G (1993) Nonlinear dynamic structures. Econometrica 61: 871–907. https://doi.org/10.2307/2951766 doi: 10.2307/2951766
[31]	Gallant AR, Rossi PE, Tauchen G (1992) A nonparametric approach nonlinear time series analysis: Estimation and Simulation, In: Parzen, E., Brillinger, D., Rosenblatt, M., et al., New dimensions in time series analysis, New York: Springer-Verlag. https://doi.org/10.1007/978-1-4613-9296-5_5
[32]	Gallant AR, Tauchen G (2010) Simulated Score Methods and Indirect Inference for Continuous Time Models, In: Aï t-Sahalia, Y., Hansen, L.P., Handbook of Financial Econometrics, North Holland, 1: 427–477. https://doi.org/10.1016/B978-0-444-50897-3.50011-0
[33]	Glosten L, Jagannathan, Runkle D (1993) Relationship between the expected value and the volatility of the nominal excess return on stocks. J Financ 48: 1779–1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x doi: 10.1111/j.1540-6261.1993.tb05128.x
[34]	Gouriéroux C (1997) ARCH Models and Financial Applications, New York: Springer.
[35]	Hamilton JD (1994) Time Series Analysis, Princeton, New Jersey: Princeton University Press. https://doi.org/10.1515/9780691218632
[36]	Hull JC (2021) Machine Learning in Business: An Introduction to the Wprld of Dats Science, GFS Press.
[37]	Koop G (1994) Parameter uncertainty and impulse response analysis. J Econom 72: 135–149. https://doi.org/10.1016/0304-4076(94)01717-4 doi: 10.1016/0304-4076(94)01717-4
[38]	Koop G, Osiewalski J, Steel MFJ (1994) Bayesian long-run prediction in time series models. J Econom 69: 61–80. https://doi.org/10.1016/0304-4076(94)01662-J doi: 10.1016/0304-4076(94)01662-J
[39]	Lee K, Pesaran MH (1993) Persistence profiles and business cycle fluctuations in a disaggregated model of UK output growth. Richerche Economiche 47: 293–322. https://doi.org/10.1016/0035-5054(93)90032-X doi: 10.1016/0035-5054(93)90032-X
[40]	Neftci S (1984) Are economic time series asymmetric over the business cycle. J Polit Econ 93: 307–328. https://doi.org/10.1086/261226 doi: 10.1086/261226
[41]	Pesaran MH, Potter S (1994) A floor and ceiling model of U.S. output. J Econ Dyn Control 21: 661–695. https://doi.org/10.1016/S0165-1889(96)00002-4 doi: 10.1016/S0165-1889(96)00002-4
[42]	Pesaran MH, Shin Y (1995) Cointegration and speed of convergence to equilibrium. J Econom 71: 117–143. https://doi.org/10.1016/0304-4076(94)01697-6 doi: 10.1016/0304-4076(94)01697-6
[43]	Pesaran MH, Pierse R, Lee K (1993) Persistence, cointegration and aggregation: A disaggregated analysis of output fluctuations in the US Economy. J Econom56: 57–88. https://doi.org/10.1016/0304-4076(93)90101-A doi: 10.1016/0304-4076(93)90101-A
[44]	Potter S (1995) A nonlinear approach to US GNP. J Appl Econom 10: 109–125. https://doi.org/10.1002/jae.3950100203 doi: 10.1002/jae.3950100203
[45]	Potter S (1994) Nonlinear impulse response functions. Department of Economics working paper (University of California, Los Angeles, CA). https://doi.org/10.2139/ssrn.163169
[46]	Ripley BD (1987) Stochastic simulation, New York: Wiley. https://doi.org/10.1002/9780470316726
[47]	Tiao G, Tsay R (1994) Some advances in nonlinear and adaptive modeling in time series analysis. J Forecast 13: 109–131. https://doi.org/10.1002/for.3980130206 doi: 10.1002/for.3980130206
[48]	Kwiatkowski D, Phillips CB, Schmidt P (1992) Testing the Null Hypothesis of Stationary against the Alternative of a Unit Root. J Econom 54: 154–179. https://doi.org/10.1111/1467-9892.00213 doi: 10.1111/1467-9892.00213
[49]	Ljung GM, Box GEP (1978) On a Measure of Lack of Fit in Time Series Models. Biometrika 66: 67–72. https://doi.org/10.1093/biomet/65.2.297 doi: 10.1093/biomet/65.2.297
[50]	Mills TC (1990) Time Series Techniques for Economists, Cambridge University Press.
[51]	Nelson D (1991) Conditional heteroscedasticity in asset returns; A new approach. Econometrica 59: 347–370. https://doi.org/10.2307/2938260 doi: 10.2307/2938260
[52]	Ramsey JB (1969) Tests for specification errors in classical least square regression analysis. J R Stat Soc Ser B-Stat Methodol 31: 350–371. https://doi.org/10.1111/j.2517-6161.1969.tb00796.x doi: 10.1111/j.2517-6161.1969.tb00796.x
[53]	Robinson PM (1983) Nonparametric Estimators for Time Series. J Time Ser Anal 4: 185–207. https://doi.org/10.1111/j.1467-9892.1983.tb00368.x doi: 10.1111/j.1467-9892.1983.tb00368.x
[54]	Rosenberg B (1972) The behavior of random variables with nonstationary variance and the distribution of security prices, unpublished paper, Research Program in Fi-nance, University of California, Berkeley.
[55]	Ross C (1989) Institutional Markets, Financial Marketing, and Financial Innovation. J Financ 44: 541–556. https://doi.org/10.1111/j.1540-6261.1989.tb04377.x doi: 10.1111/j.1540-6261.1989.tb04377.x
[56]	Scheinkman JA (1990) Nonlinearities in Economic Dynamics. Econ J 100: 33–48. https://doi.org/10.2307/2234182 doi: 10.2307/2234182
[57]	Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6: 461–464. https://doi.org/10.1214/aos/1176344136 doi: 10.1214/aos/1176344136
[58]	Shepard N (2004) Stochastic Volatility: Selected Readings, Oxford University Press, https://doi.org/10.1093/oso/9780199257195.001.0001
[59]	Sims C (1980) Macroeconomics and Reality. Econometrica 48: 1–48. https://doi.org/10.2307/1912017 doi: 10.2307/1912017
[60]	Solibakke PB (2020) Stochastic Volatility Models Predictive Relevance for Equity Markets, In: Valenzuela, O., Rojas, F., Herrera, L.J., et al., Theory and Applications of Time Series Analysis: Selected Contributions from ITISE 2019, 1st ed., Springer, Cham, 125–143. https://doi.org/10.1007/978-3-030-56219-9_9
[61]	Solibakke Per B (2022) Bootstrapped Nonlinear Impulse-Response Analysis: The FTSE100 (UK) and the NDX100 (US) Indices 2012–2021. Int J Comput Econ Econom 12: 197–221. https://doi.org/10.1504/IJCEE.2021.10043332 doi: 10.1504/IJCEE.2021.10043332
[62]	Tauchen G, Pitts M (1983) The price variability volume relationship on speculative markets. Econometrica, 485–505. https://doi.org/10.2307/1912002 doi: 10.2307/1912002
[63]	Taylor S (1982) Financial returns modelled by the product of two stochastic processes—a study of daily sugar prices 1961–79, In: Anderson, O. D.(ed.), Time Series Analysis: Theory and Practice, Amsterdam, North-Holland, 1: 203–226. https://doi.org/10.1093/oso/9780199257195.003.0003
[64]	Taylor S (2005) Asset Price Dynamics, Volatility, and Prediction, Princeton University Press, https://doi.org/10.1515/9781400839254
[65]	Vo M (2011) Oil and Stock market volatility: A multivariate stochastic volatility perspective. Energy Econ 33: 956–965. https://doi.org/10.1016/j.eneco.2011.03.005 doi: 10.1016/j.eneco.2011.03.005

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