Modelling Rainfall Patterns using SARIMA Model: a Case Study of Nyeri County in Kenya

The paper investigated the time series components, and to build appropriate model to forecast the rainfall of Nyeri county using monthly data from January, 1983 to December, 2015. The descriptive statistics of the rainfall showed that the highest amount of rainfall was recorded in April 1997 while the lowest amount of rainfall was recorded in September 1983. The time series rainfall data was decomposed into stochastic trend, seasonal variations and remainder. The time series of the yearly data showed decreasing trend. The rainfall data was found to be stationary and that was confirmed using dickey fuller test which yielded a test value of 6.5013 and a p-value of 0.01. The appropriate orders of models were picked based on results of ACF and PACF plots and evaluated using Akaike Information Criterion and Bayesian Information criterion. The best model was found to be SARIMA(1,0,0)(3,0,0)12 with AIC 1944.7 and BIC 1964.46. The model residuals showed normality as most points fell on the quantile-quantile line with few close to it. The residuals also confirmed white noise. From the model validation results,the predicted values were well-fitted through the original data with lower and upper confidence limits containing majority of the original data. The RMSE of out-sample was less than that of the in-sample with values of 7.6579 and 54.6680 respectively. This showed that the identified SARIMA model was suitable for predicting rainfall of Nyeri County.