Application of Seasonal Autoregressive Moving Average Models to Analysis and Forecasting of Time Series Monthly Rainfall Patterns in Embu County, Kenya

Abstract

Rainfall is of critical importance for many people, particularly those whose livelihoods depend on rain-fed agriculture. Predicting the trend of rainfall is a difficult task, and statistical approaches such as time series analysis provide a means for predicting the patterns of rainfall. The models also offer the potential to improve areas such as increased food production, profitability, and improved food security policing. However, these forecasts and information systems may, in some instances, not be suitable for direct use by stakeholders in their decision-making. The objective of this study was to investigate rainfall variability and develop a Seasonal Auto-Regressive Integrated Moving Average (SARIMA) model for fitting the monthly rainfall using time series data. Secondary monthly data from 1998 to 2017 for Embu County was collected from the Kenya Meteorological Department, Embu and recorded into an excel sheet. R-software was utilized to analyse data for descriptive statistics, rainfall variability, and model fitting. The coefficient of variation for annual and seasonal rainfall was calculated. The Box Jenkin's ARIMA modelling procedure (model identification, model estimation, model validation) was used to determine the best models for the data. The main study findings indicated the existence of annual variability of 34%, March-April-May rainfall variability of 44%, and October-November-December variability of 44%. A first-order differenced SARIMA (1, 1, 1) (0, 1, 2)12 model with an AIC score of 9.99356 was found suitable for predicting rainfall pattern in Embu, County. The study outcome revealed that Embu County experiences high seasonal and rainfall variation of rainfall, thus requires a reliable model for better prediction.