Construction of Dependence Structure for Rainfall Stations by Joining Time Series Models with Copula Method




Bivariate copula, time series models, dependence modelling, non-stationary, rainfall


Copula model has applied in various hydrologic studies, however, most analyses conducted does not considering the non-stationary conditions that may exist in the time series. To investigate the dependence structure between two rainfall stations at Johor Bahru, two methods have been applied. The first method considers the non-stationary condition that exists in the data, while the second method assumes stationarity in the time series data.  Through goodness-off-fit (GOF) and simulation tests, performance of both methods are compared in this study. The results obtained in this study highlight the importance of considering non-stationarity conditions in the hydrological data.

Author Biographies

Rahmah Mohd Lokoman, Universiti Teknologi Malaysia

Postgraduate student

Department of Mathematics,Faculty of Science.

Fadhilah Yusof, Universiti Teknologi Malaysia

Prof. Dr.

Department of Mathematics,
Faculty of Science.

Nor Eliza Alias, Universiti Teknologi Malaysia


Department of Hydraulics and Hydrology,
Faculty of Civil Engineering.

Zulkifli Yusop, Universiti Teknologi Malaysia

Prof. Dr.

Centre for Environmental Sustainability and Water Security.


G. Salvadori and C. De Michele, “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events”, Water Resources Research, vol. 40, no. 12, W12511, 2004.

A. Sklar, “Fonctions de répartition à n dimensions et leurs marges”, Publications de l’Institut de Statistique de L’Université de Paris, vol. 8, pp. 229-231, 1959.

L. Zhang and V. P. Singh, “Bivariate rainfall frequency distributions using Archimedean copulas”, Journal of Hydrology, vol. 332, no. 1-2, pp. 93-109, 2007.

R.B. Nelsen, “An Introduction to Copulas”, Springer, New York, 2006.

F. Yusof, I. L. Kane and Z. Yusop, “Hybrid of ARIMA-GARCH Modeling in Rainfall Time Series”, Jurnal Teknologi, vol. 63, no. 2, pp. 27–34, 2013.

R. T. A. de Oliveira, T. F. Oliveira, P. R. A. Firmino and T. A. E. Ferreira, “Combining Time Series Forecasting Models via Gumbel-Hougaard Copulas”, BRICS Congress on Computational Intelligence and 11th Brazilian Congress on Computational Intelligence, pp. 568-573, 2013.

R.T.A. de Oliveira, T.F.O. de Assis, P. R. A. Firmino and T. A. E. Ferreira, “Copulas-based time series combined forecasters”, Information Sciences, vol. 376, pp. 110–124, 2017.

N.M. Ariff, A.A. Jemain, K. Ibrahim and W.Z. Wan Zin, “IDF relationships using bivariate copula for storm events in Peninsular Malaysia”, Journal of Hydrology, vol. 470-471, pp. 158-171, 2012.

F. Yusof, F. H. Mean, S. Jamaludin and Z. Yusop, “Characterization of Drought Properties with Bivariate Copula Analysis”, Water Resource Management, vol. 27, pp. 4183-4207, 2013.

K. C. Yee, S. Jamaludin., F. Yusof and F. H. Mean, “Bivariate copula in fitting rainfall data”, AIP Conference Proceedings, vol. 1605, no. 1, pp. 986-990, 2014.

K. A. Kili, (2017, Nov 09), “Several areas in JB hit by flash floods”, The Star Online. Retrieved from

A. F. Othman, (2017, Nov 14), “Flash floods hit several parts of Johor; bad weather predicted across 8 other states”, New Straits Times. Retrieved from

B. Tan, (2017, Nov 09), “Five areas in Johor Baru hit by flash floods”, Malay Mail. Retrieved from

T. Bollerslev, “Generalized Autoregressive Conditional Heteroscedasticity”, Journal of Econometrics, vol. 31, pp. 307-327, 1986.

I.L. Kane and F. Yusof, “Assessment of Risk of Rainfall Events with a Hybrid of ARFIMA-GARCH”, Modern Applied Science, vol. 7, no. 12, pp.78-89, 2013.

H. Chen, Q. Wan, F. Li and Y. Wang, “GARCH in mean type models for wind power forecasting”, IEEE Power and Energy Society General Meeting, pp. 1-5, 2013.