Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model

Abstract

Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today’s world. The objective of this study was to conducted a diagnostic analyzes of weather variables which were used to model the rainfall patterns by use of Bayesian Vector Autoregressive (BVAR). The diagnostic analyzes was done after the normalization of the data. The data was found to be stable after first differencing and it was tested using Augmented Dicker Fuller (ADF) and Phillips-Perron (PP) test. The tests were found to have the P-values that were statistically significant. The Granger Causality test was also conducted and found to be statistically significant. The Ljung-Box test of residuals, shows that the graphs of these residuals produced, appeared to explain all the available information in the forecasted model. The mean of the residuals was near to zero and therefore no significant correlation was witnessed. The time plot shows that the variation of the residuals remains much the same across the historical data, apart from the two values that were beyond 0.2 or -0.2 in Zone Two, and therefore the residual variance was treated as constant. The histogram shows that the residuals were normally distributed, which represented gaussian behavior. The ACF graph, shows that the spikes were within the required limits, so the conclusion was that the residuals had no autocorrelation of the residuals. The Ljung-Box test shows that the developed model was good for forecasting. Finally, the researcher recommends application of other techniques like Random Forest and Bootstrapping technique to check whether the accuracy may further be improved from other models.