Application of bayesian vector autoregressive model in forecasting rainfall pattern in Kenya.

Abstract

Time series modelling is of fundamental importance in forecasting weather that is basically one of the most technologically and scientifically challenging problems around the world currently. To make an accurate prediction is certainly one of the key challenges that meteorologists are facing all over the world. One of the most affected areas is the rainfall patterns, which is being influenced by global warming, causing drastic changes in its patterns that are characterized by either very high or low precipitation and temperature. These extreme changes have been identified as major global challenges of recent times. Meteorological scientist always tries to find means to understand the atmosphere of the Earth, and to develop accurate weather prediction models. Several methods have been used in weather prediction, which includes, Classical vector Autoregressive (VAR) models which perform only polynomial-time computation to compute the probability of the next fixed model parameters. While this is attractive, it means they cannot model distributions with a time varying data. They also have a problem with the curse of dimensionality. Recently, machine learning methods are assumed to be accurate techniques and have been widely used as an alternative to classical methods for weather prediction. With all these powerfulness and popularity machine learning methods are not perfect. They have several limitations where they require; massive datasets, enough time and resources, does not work well with high dimensional data and have high error vulnerability among others. Despite the availability of different models that are used by the meteorologists and other departments to make predictions, the same devastating scenarios of unpredictable weather changes are still being experienced. Therefore, robust models reliable for accurate predictions are needed on short- and long-term time scales to reduce potential risks and damages that may occur due to unexpected weather changes. These short comings are well addressed by the Bayesian Vector Autoregressive (BVAR) models. The purpose of this study was to develop a BVAR model for predicting rainfall patterns in Kenya. The specific objectives were to; perform diagnostic analysis of the weather variables; develop Bayesian Vector Autoregressive predictive model; conduct model performance analysis and apply the model to forecast the rainfall patterns in Kenya. The Augmented Dicker Fuller and Granger Causality tests were used for diagnostic analysis. The research adopted secondary data for a period of four years (2014-2018), which was sourced from Trans-African Hydro-Meteorological Observatory (TAHMO) and Kenya Meteorological stations. Bayesian Vector Autoregressive model was developed using multiple regression analysis in a system of equations. The model imposes structures through information prior beliefs on the parameters which were obtained from VAR models, likelihood models between the true parameters and the measured variables and the posterior distribution which is the conditional distribution of the parameter given the measurements. The model sensitivity was performed using the confusion matrix. The F-test was used to compare the variances of the actual and the predicted rainfall values. The data was analyzed using R-Statistical Software. The study found that; the data variables were stationary after at least the first differencing. Temperature, atmospheric pressure, wind speed and relative humidity were statistically significant (p < 0.05) determinants of rainfall in all five zones, while wind gust and radiation were significant in two zones, coast and arid areas. The BVAR model developed was statistically significant (R 2 = 0.9896). The performance of the model was adequate (RMSE= 86.81%) and its sensitivity was 82.52%, making it appropriate for forecasting. There was no significant difference between the variances of the actual and predicted values of rainfall (p = 0.3893) at the 5% level of significance in zone five. The study made the following conclusion, after at least the one differencing the weather variables were found to be stable, the developed model coefficients were found to be statistically significant, the model performance was good and it forecasting ability was termed as high. In conclusion, the Bayesian Vector Autoregressive model developed is suitable for forecasting rainfall patterns in Kenya. The study recommends adoption of the BVAR model by relevant authorities to predict rainfall. For further research the study recommends for use of more weather variables to make more accurate prediction. The study also recommends for development of dynamic weather model, which tests for the impulse response of weather variable in respect to change in other endogenous variables.