TESTING VOLATILITY PERSISTENCE WITH FRACTIONAL INTEGRATIONAND COINTEGRATION IN WORLDWIDE COMMODITY MARKETS

Authors

  • Mariam Kamal Basque Country University, Bilbao, Spain
  • Luis Alberiko Gil-Alana University of Navarra, Pamplona, Spain and Universidad Francisco de Vitoria, Madrid, Spain

DOI:

https://doi.org/10.58885/ijbe.v08i2.032.mk

Keywords:

volatility, commodity crisis, commodity prices, persistence, fractional integration, fractional cointegration.

Abstract

In this paper, we examine the volatility of commodity prices around the world using monthly data for the time period 1960–2022. During this period, there were significant economic crises that increased the prices of both energy and non-energy commodities in the short term. These past crises may provide insights into the behavior of current crises, as they generally exhibit similar patterns. We use fractional integration methods and find that the volatility for each variable exhibits mean reversion, with the effect of the shocks disappearing in the long run. While this may seem obvious, our paper is the first to empirically demonstrate this significant process of convergence using a flexible time series model. As an additional contribution, we complement our analysis by incorporating a fractional cointegration test to examine potential relationships among the commodity prices. Our findings reveal the existence of four distinct cointegrating relationships within the set of ten commodity prices. This implies that these commodities are not entirely independent and may share underlying connections that contribute to their price movements over time. This valuable insight further enriches our understanding of the intricate interactions within the commodity market. We conclude that although countries do not have effective policies for mitigating volatility, it is only a short-term phenomenon that will disappear in the long term.

References

Abbritti, M., L.A. Gil-Alana, Y. Lovcha and A. Moreno (2016). Term structure persistence, Journal of Financial Econometrics 14, 2, 331-352.

https://doi.org/10.1093/jjfinec/nbv003

Abbritti, M., Carcel, H., Gil-Alana, L.A. & Moreno, A. (2023). Term premium in a fractionally cointegrated yield curve. Journal of Banking and Finance, Volume 149, 106777. https://doi.org/10.1016/j.jbankfin.2023.106777

Bakas, D., & Triantafyllou, A.G. (2020). Commodity price volatility and the economic uncertainty of pandemics. Economics Letters, 193, issue C, number S0165176520301890. https://doi.org/10.1016/j.econlet.2020.109283

Barani, S., Cristofaro, L., Gil-Alana, L.A., Taroni, M. and Ferretti, G. (2021). Long memory in earthquakes time series. Evidence from induced sysmology, Frontiers in Earth Science. Solid Earth Geophysics 9. https://doi.org/10.3389/feart.2021.563649

Beck, S. (2001). Autoregressive conditional heteroscedasticity in commodity spot prices. Journal of Applied Econometrics, 16(2), 115-132. https://doi.org/10.1002/jae.591

Baffes, J. & Nagle, P. (Eds.). (2022). Commodity Markets: Evolution, Challenges, and Policies. World Bank Publications.

BOOK: Commodity Markets: Evolution, Challenges, and Policies

Bloomfield, P. (1973). An exponential model in the spectrum of a scalar time series, Biometrika 60, 2, 217–226. https://doi.org/10.1093/biomet/60.2.217

Brooks, C., & Prokopczuk, M. (2013). The dynamics of commodity prices. Quantitative Finance, 13(4), 527-542. https://doi.org/10.1080/14697688.2013.769689

Cashin, P., McDermott, C. J., & Scott, A. (2002). Booms and slumps in world commodity prices. Journal of Development Economics, 69(1), 277-296. https://doi.org/10.1016/S0304-3878(02)00062-7

Casoli, C., & Lucchetti, R. (2022). Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices, The Econometrics Journal, Volume 25, Issue 2. Pages 494–514. https://doi.org/10.1093/ectj/utab034

Cavalcanti, T., Mohaddes, K., & Raissi, M. (2015). Commodity price volatility and the sources of growth. Journal of Applied Econometrics, 30 (6), 857-873. https://doi.org/10.1002/jae.2407

Chevallier, J., & Ielpo, F. (2014). Twenty years of jumps in commodity markets. International Review of Applied Economics, 28(1), 64-82.

https://doi.org/10.1080/02692171.2013.826637

Ciaian, P. (2011). Interdependencies in the energy–bioenergy–food price systems: A cointegration analysis. Resource and energy Economics, 33(1), 326-348. https://doi.org/10.1016/j.reseneeco.2010.07.004

Dickey, D.A. & Fuller, W.A. (1979). Distribution of the Estimators for Autoregressive Time Series With a Unit Root, Journal of the American Statistical Association 74, 366, 427-431. https://doi.org/10.1080/01621459.1979.10482531

Diewald, L., Prokopczuk, M., & Wese Simen, C. (2015). Time-variations in commodity price jumps. Journal of Empirical Finance, 31, 72-84.

https://doi.org/10.1016/j.jempfin.2015.02.004

Duffie, D., Gray, S., & Hoang, P. (1999). Volatility in energy prices. United Kingdom: Risk Books.

BOOK: INIS Repository Search - Single Result (iaea.org)

Engle, Robert F. and Granger, C.W.J. Cointegration and error correction: representation, estimations and testing. Econometrica. Vol.55, No.2. 1987. pp. 251-276. https://doi.org/10.2307/1913236

Geman, H. (2007). Mean reversion versus random walk in oil and natural gas prices. In M.C. Fu, R.A. Jarrow, J. Y. J. Yen, & R. J. Elliott (Eds.). Advances in Mathematical Finance (pp. 169-180). Applied and Numerical Harmonic Analysis. Birkhäuser Boston.

BOOK: Mean Reversion Versus Random Walk in Oil and Natural Gas Prices. SpringerLink

Ghoshray, A. (2019). Do international primary commodity prices exhibit asymmetric adjustment?. Journal of Commodity Markets, 14, 40-50. https://doi.org/10.1016/j.jcomm.2018.08.002

Gil-Alana, L.A., and Robinson, P.M. (1997). Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. Journal of Econometrics, 80, 241-268. https://doi.org/10.1016/S0304-4076(97)00038-9

Granger, C.W.J., (1966). The Typical Spectral Shape of an Economic Variable. Econometrica 34(1), 150-161. https://doi.org/10.2307/1909859

Granger, C.W.J., (1980). Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14, 227–38.

https://doi.org/10.1016/0304-4076(80)90092-5

Granger, C.W.J., (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16, 121–30. https://doi.org/10.1016/0304-4076(81)90079-8

Granger, C.W.J., and Joyeux, R. (1980). An Introduction to Long-Memory Time Series Models and Fractional Differencing. Journal of Time Series Analysis, 1, 15-39. https://doi.org/10.1111/j.1467-9892.1980.tb00297.x

Granger, C.W.J. & Ding, Z. (1995). Some Properties of Absolute Return: An Alternative Measure of Risk, Annales d'Économie et de Statistique 40, 67-91. https://doi.org/10.2307/20076016

Hagen, J.V. (1989). Relative commodity prices and cointegration. Journal of Business & Economic Statistics, 7(4), 497-503.

https://doi.org/10.1080/07350015.1989.10509763

Hosking, J.R.M. (1981). Fractional differencing. Biometrika, 68, 165-76. https://doi.org/10.2307/2335817

Jacks, D.S., O'Rourke, K.H., & Williamson, J.G. (2011). Commodity price volatility and world market integration since 1700. Review of Economics and Statistics, 93(3), 800-813. https://doi.org/10.1162/REST_a_00091

Joëts, M., Mignon, V., & Razafindrabe, T. (2017). Does the volatility of commodity prices reflect macroeconomic uncertainty? Energy Economics, 68, 313-326. https://doi.org/10.1016/j.eneco.2017.09.017

Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, Vol. 12, No. 2–3, pp. 231–254. 18. https://doi.org/10.1016/0165-1889(88)90041-3

Johansen, S., and Juselius, K. (1990). Maximum Likelihood Estimation and Inference on Cointegration–with Applications to the Demand for Money. Oxford Bulletin of Economics and Statistics, Vol. 52, No. 2, pp. 169–210.

https://doi.org/10.1111/j.1468-0084.1990.mp52002003.x

Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, Vol. 59, No. 6, pp. 1551–1580. https://doi.org/10.2307/2938278

Johansen, S. (1995). Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. New York: Oxford University Press.

https://doi.org/10.1093/0198774508.001.0001

Johansen, S. (2008). A representation theory for a class of vector autoregressive models for fractional processes. Econometric Theory, 24, 651-676. https://doi.org/10.1017/S0266466608080274

Johansen, S., & Nielsen, M.O. (2010). Likelihood inference for a nonstationary fractional autoregressive model. Journal of Econometrics, 158, 51-66. https://doi.org/10.1016/j.jeconom.2010.03.006

Johansen, S., & Nielsen, M.O. (2012). Likelihood inference for a fractionally cointegrated vector autoregressive model. Econometrica, 80, 2667-2732. https://doi.org/10.3982/ECTA9299

Johansen, S., & Nielsen, M.O. (2014). The role of initial values in nonstationary fractional time series models (QED Working Paper No. 1300). Kingston, Ontario, Canada: Queen’s. University. https://www.econ.ku.dk/english/research/publications/wp/dp_2012/1218.pdf/

Karbuz, S., & Jumah, A. (1995). Cointegration and commodity arbitrage. Agribusiness, 11(3), 235-243.

https://doi.org/10.1002/1520-6297(199505/06)11:3<235::AID-AGR2720110305>3.0.CO;2-P

Lombardi, M.J., & Ravazzolo, F. (2016). On the correlation between commodity and equity returns: Implications for portfolio allocation. Journal of Commodity Markets, 2(1), 45-57. https://doi.org/10.1016/j.jcomm.2016.07.005

Nazlioglu, S., & Soytas, U. (2012). Oil price, agricultural commodity prices, and the dollar: A panel cointegration and causality analysis. Energy Economics, 34(4), 1098-1104. https://doi.org/10.1016/j.eneco.2011.09.008

Nguyen, D.B.B., & Prokopczuk, M. (2019). Jumps in commodity markets. Journal of Commodity Markets, 13, 55-70. https://doi.org/10.1016/j.jcomm.2018.10.002

Ohashi, K., & Okimoto, T. (2016). Increasing trends in the excess comovement of commodity prices. Journal of Commodity Markets, 1(1), 48-64. https://doi.org/10.1016/j.jcomm.2016.02.001

Perez de Gracia, F., L.A. Gil-Alana and R. Mudida (2014). Persistence, long memory and seasonality in Kenyan tourism time series, Annals of Tourism Research 45, 89-101. https://doi.org/10.1016/j.annals.2014.02.008

Phillips, P.C.B., Perron, P. (1988). Testing for a Unit Root in Time Series Regression. Biometrika. 75 (2): 335–346.

https://doi.org/10.1093/biomet/75.2.335

Pindyck, R. (2001). The dynamics of commodity spot and futures markets: A primer. Energy Journal, 22(3):1–29, 2001. https://doi.org/10.5547/ISSN0195-6574-EJ-Vol22-No3-1

Prokopczuk, M., Symeonidis, L., & Wese Simen, C. (2016). Do jumps matter for volatility forecasting? Evidence from energy markets. Journal of Futures Markets, 36(8), 758-792. https://doi.org/10.1002/fut.21759

Robinson, P. (1978). Statistical inference for a random coefficient autoregressive model, Scandinavian Journal of Statistics 5, 163-168.

http://eprints.lse.ac.uk/id/eprint/1454

Robinson, P. (1994). Efficient Tests of Nonstationary Hypotheses. Journal of the American Statistical Association, 89, 1420-1437.

https://doi.org/10.1080/01621459.1994.10476881

Samuelson, P. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41-49.

https://doi.org/10.1142/9789814566926_0002

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Published

2023-09-05

How to Cite

Mariam Kamal, & Luis Alberiko Gil-Alana. (2023). TESTING VOLATILITY PERSISTENCE WITH FRACTIONAL INTEGRATIONAND COINTEGRATION IN WORLDWIDE COMMODITY MARKETS. International Journal of Business & Economics (IJBE), 8(2), 32–51. https://doi.org/10.58885/ijbe.v08i2.032.mk

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