Modelling Monthly Rainfall Data of Port Harcourt, Nigeria by Seasonal Box-Jenkins Methods

Author(s): Ette Harrison Etuk, Imoh Udo Moffat, Benjamin Ele Chims

Brief review of literature of the well documented seasonal Box-Jenkins modelling is done. Rainfall is a seasonal phenomenon the world over. For illustrative purposes, monthly rainfall as measured in Port Harcourt, Nigeria, is modelled by a (5, 1, 0)x(0, 1, 1)12 seasonal ARIMA model. The time-plot shows no noticeable trend. The known and expected seasonality is clear from the plot. Seasonal (i.e. 12-point) differencing of the data is done, then a nonseasonal differencing is done of the seasonal differences. The correlogam of the resultant series reveals the expected 12-monthly seasonality, and the involvement of a seasonal moving average component in the first place and a nonseasonal autoregressive component of order 5. Hence the model mentioned above. The adequacy of the modelled has been established.

Seasonal Time Series, ARIMA model, rainfall, Port Harcourt

1. Box, G. E. P. and Jenkins, G. M. (1976).” Time Series Analysis, Forecasting and Control”, Holden-Day, San Francisco
2. Madsen, H. (2008).” Time Series Analysis”, Chapman & Hall/CRC, London
3. Etuk, E. H. (2013). A Seasonal Time Series for Nigerian Monthly Air Traffic Data. International of Review and Research in Applied Sciences, 14, 3, pp. 596 – 602
4. Osarumwense, O.I. (2013). Applicability of Box Jenkins SARIMA Model in Rainfall Forecasting: A Case Study of Port-Harcourt South South Nigeria. Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering amd Medicine, 4, 1, pp. 1-4-
5. Olofintoye, O. O. And Sule, B. F. (2010). Impact of Global Warming on the Rainfall and Temperature in the Niger Delta of Nigeria. USEP-Journal of Research Information in Civil Engineering, 7, 2, pp. 33 – 48
6. Chiadikobi, K. C., Omoboriowo, A. O., Chiaganam, O. I., Opatola, A. O. And Oyebanji, O. (2011). Flood Risk Assessment of Port Harcourt, Rivers State, Nigeria. Advances in Applied Research, 2, 6: pp. 287 – 298
7. Dike, B. U. And Nwachukwu, B. A. (2003). Analysis of Nigerian Hydrometeoroligical Data. Nigerian Journal of Technology, 22, 1, pp. 29 – 38
8. Salako, F. K. (2007). Rainfall seasonality in the Niger Delta Belt, Nigeria. Journal of Geography and Regional, 52, 2, pp. 51 – 60
9. Oyetunji, O. B. (1985).” Inverse Autocorrelations and Moving Average Time Series Modelling”. Journal of Official Statistics, 1, pp. 315 – 322
10. Etuk, E. H. (1987). On the Selection of Autoregressive Moving Average Models. An unpublished Ph. D. Thesis, Department of Statistics, University of Ibadan, Nigeria
11. Etuk, E. H. (1998).” An Autoregressive Integrated Moving Average (ARIMA) Model: A Case Study”. Discovery and Innovation, 10, 1 & 2, pp. 23 – 26