An assessment of Box-Jenkins models: Forcados monthly rainfall as case study

Abstract

An autoregressive Box-Jenkins stochastic model of the twelfth order has been developed for the monthly rainfall data for Forcados along the coast of South Eastern Nigeria. The goodness of fit of the model was assessed by estimating the autocorrelations of the residuals of the historical data (from January 1931 to December 1960) for lags one to twelve. A 95% confidence band was also established for the autocorrelations. The results show that eleven of the twelve autocorrelations fall within the 95% confidence band, which makes the model just barely acceptable. Box and Jenkins (1972) indicate that any of their models can in fact be shown to be equivalent to an infinite Autoregressive model (or Moving Average model for that matter) and since also monthly rainfall data are known to exhibit a seasonality of twelve months, the performance of an Autoregressive model of the twelfth order is indicative of that of Box-Jenkins models in general for monthly rainfall modeling. The factors that influence the suitability of a model include the nature of the physical processes involved and the quality of the data available. The use of Box-Jenkins models to simulate monthly rainfall in the coastal part of Nigeria appear to be just barely acceptable. It would thus be worthwhile to investigate other models.

Keywords: Rainfall, Stochastics, Autoregression, Residuals

Journal of Applied Science, Engineering and Technology, Volume 10, 60-65