@phdthesis{Karama2021,
  author    = {Karama, Alphonse},
  title     = {East African Seasonal Rainfall prediction using multiple linear regression and regression with ARIMA errors models},
  doi       = {10.25972/OPUS-25183},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-251831},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {The detrimental impacts of climate variability on water, agriculture, and food resources in East Africa underscore the importance of reliable seasonal climate prediction. To overcome this difficulty RARIMAE method were evolved. Applications RARIMAE in the literature shows that amalgamating different methods can be an efficient and effective way to improve the forecasts of time series under consideration. With these motivations, attempt have been made to develop a multiple linear regression model (MLR) and a RARIMAE models for forecasting seasonal rainfall in east Africa under the following objectives: 1. To develop MLR model for seasonal rainfall prediction in East Africa. 2. To develop a RARIMAE model for seasonal rainfall prediction in East Africa. 3. Comparison of model's efficiency under consideration In order to achieve the above objectives, the monthly precipitation data covering the period from 1949 to 2000 was obtained from Climate Research Unit (CRU). Next to that, the first differenced climate indices were used as predictors. In the first part of this study, the analyses of the rainfall fluctuation in whole Central- East Africa region which span over a longitude of 15 degrees East to 55 degrees East and a latitude of 15 degrees South to 15 degrees North was done by the help of maps. For models' comparison, the R-squared values for the MLR model are subtracted from the R-squared values of RARIMAE model. The results show positive values which indicates that R-squared is improved by RARIMAE model. On the other side, the root mean square errors (RMSE) values of the RARIMAE model are subtracted from the RMSE values of the MLR model and the results show negative value which indicates that RMSE is reduced by RARIMAE model for training and testing datasets. For the second part of this study, the area which is considered covers a longitude of 31.5 degrees East to 41 degrees East and a latitude of 3.5 degrees South to 0.5 degrees South. This region covers Central-East of the Democratic Republic of Congo (DRC), north of Burundi, south of Uganda, Rwanda, north of Tanzania and south of Kenya. Considering a model constructed based on the average rainfall time series in this region, the long rainfall season counts the nine months lead of the first principal component of Indian sea level pressure (SLP_PC19) and the nine months lead of Dipole Mode Index (DMI_LR9) as selected predictors for both statistical and predictive model. On the other side, the short rainfall season counts the three months lead of the first principal component of Indian sea surface temperature (SST_PC13) and the three months lead of Southern Oscillation Index (SOI_SR3) as predictors for predictive model. For short rainfall season statistical model SAOD current time series (SAOD_SR0) was added on the two predictors in predictive model. By applying a MLR model it is shown that the forecast can explain 27.4\% of the total variation and has a RMSE of 74.2mm/season for long rainfall season while for the RARIMAE the forecast explains 53.6\% of the total variation and has a RMSE of 59.4mm/season. By applying a MLR model it is shown that the forecast can explain 22.8\% of the total variation and has a RMSE of 106.1 mm/season for short rainfall season predictive model while for the RARIMAE the forecast explains 55.1\% of the total variation and has a RMSE of 81.1 mm/season. From such comparison, a significant rise in R-squared, a decrease of RMSE values were observed in RARIMAE models for both short rainfall and long rainfall season averaged time series. In terms of reliability, RARIMAE outperformed its MLR counterparts with better efficiency and accuracy. Therefore, whenever the data suffer from autocorrelation, we can go for MLR with ARIMA error, the ARIMA error part is more to correct the autocorrelation thereby improving the variance and productiveness of the model.},
  subject      = {Regression},
  language  = {en}
}