Conditional Heteroscedasticity in Streamflow Process: Paradox or Reality?


The various physical mechanisms governing the dynamics of streamflow processes act on a seemingly wide range of temporal and spatial scales; almost all the mechanisms involved present some degree of nonlinearity. Against the backdrop of these issues, in this paper, attempt was made to critically look at the subject of Autoregressive Conditional Heteroscedasticity (ARCH) or volatility of streamflow processes, a form of nonlinear phenomena. Towards this end, streamflow data (both daily and monthly) of the River Benue, Nigeria were used for the study. Results obtained from the analyses indicate that the existence of conditional heteroscedasticity in streamflow processes is no paradox. Too, ARCH effect is caused by seasonal variation in the variance for monthly flows and could partly explain same in the daily streamflow. It was also evident that the traditional seasonal Autoregressive Moving Average (ARMA) models are inadequate in describing ARCH effect in daily streamflow process though, robust for monthly streamflow; and can be removed if proper deseasonalisation pre-processing was done. Considering the findings, the potential for a hybrid Autoregressive Moving Average (ARMA) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH)type models should be further explored and probably embraced for modelling daily streamflow regime in view of the relevance of statistical modelling in hydrology.

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M. Otache, I. Ahaneku, A. Mohammed and J. Musa, "Conditional Heteroscedasticity in Streamflow Process: Paradox or Reality?," Open Journal of Modern Hydrology, Vol. 2 No. 4, 2012, pp. 79-90. doi: 10.4236/ojmh.2012.24010.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] W. Wang, P. H. A. J. M. Van Gelder, J. K. Verjling and J. Ma, “Testing and Modelling. Autoregressive Conditional Heteroscedasticity of Streamflow Processes,” Nonlinear Processes in Geophysics, Vol. 12, 2005, pp. 55-66. doi:10.5194/npg-12-55-2005
[2] V. Livina, Y. Ashkenazy, Z. Kizner, V. Strygin, A. Bunde and S. Havlin, “A Stochastic Model of River Discharge Fluctuations,” Physica A, Vol. 330, No. 1-2, 2003, pp. 283290. doi:10.1016/j.physa.2003.08.012
[3] M. Y. Otache, “Contemporary Analysis of Benue River flow Dynamics and Modelling,” Ph.D. Dissertation, Hohai University, Nanjing, 2008.
[4] M. Y. Otache, A. S. Mohammed and I. E. Ahaneku, “Nonlinear Deterministic Chaos in Benue River flow Daily Time Series,” Journal of Water Resource and Protection, Vol. 3, No. 10, 2011, pp. 747-757.
[5] T. Bollerslev, “Generalized Autoregressive Conditional Heteroscedasticity,” Journal of Econometrics, Vol. 31, No. 3, 1986, pp. 307-327. doi:10.1016/0304-4076(86)90063-1
[6] N. T. Kottegoda, “Stochastic Water Resources Technology,” The Macmillan Press Ltd., London, 1980.
[7] C. W. J. Granger and A. P. Andersen, “An Introduction to Bilinear Time Series Models,” Vandenhoeck and Ruprecht, Gottingen, 1978.
[8] A. A. Weiss, “ARMA Models with ARCH Errors,” Journal of Time Series Analysis, Vol. 5, No. 2, 1984, pp. 129143. doi:10.1111/j.1467-9892.1984.tb00382.x
[9] M. A. Hauser and R. M. Kunst, “Fractionally Integrated Models with ARCH Errors: With an Application to the Swiss 1-Month Euromarket Interest Rate,” Review of Quantitative Finance and Accounting, Vol. 10, No. 1, 1998, pp. 95-113. doi:10.1023/A:1008252331292
[10] R. J. S. Tol, “Autoregressive Conditional Heteroscedasticity in Daily Temperature Measurements,” Environmetrics, Vol. 7, No. 1, 1996, pp. 67-75. doi:10.1002/(SICI)1099-095X(199601)7:1<67::AID-ENV164>3.0.CO;2-D
[11] A. Bera and M. Higgins, “On ARCH Models: Properties, Estimation, and Testing,” In: L. Oxley, D. A. R. George, C. J. Roberts and S. Sayer, Eds., Surveys in Econometrics, Blackwell Press, Oxford, Cambridge, 1995, pp. 171-224.

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