ABSTRACT
For
many years planning and management of water resources involved modeling and
simulation of temporally sequenced and stochastic hydrologic events. Rainfall process is one of such hydrologic events
which calls for time series analysis to better understand interesting features
contained in it. Many statistics-based methods are available to simulate and
predict such a kind of time series. Autoregressive (AR), moving average (MA), autoregressive
moving average (ARMA) and autoregressive integrated moving average (ARIMA)
models are among those methods. In this study a search was conducted to
identify and examine a capable stochastic model for annual rainfall series
(over the period 1954-2015) of Debre Markos town, Ethiopia. For the historical
series, normality and stationarity tests were conducted to check if the time series
was from a normally distributed and stationary process. Shapiro-Wilk (SW),
Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests were among the
normality tests conducted whereas, Augmented Dickey-Fuller (ADF), Phillips-Perron
(PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests were among the
stationarity tests. Based on the test results, logarithmic transformation and
first order differencing were performed to bring the original series to a
normal and stationary series. Results of model fitting showed that three models
namely, AR (2), MA (1) and ARMA (2,1) were capable in describing the annual
rainfall series. A diagnostic check was performed on model residuals and ARMA
(2,1) was found to be the best model among the candidates. Furthermore, three
information criteria: Akaike Information Criterion (AIC), the corrected Akaike Information
Criterion (AICc) and Bayesian Information Criterion (BIC) were used to select
the best model. In this regard, too, the least information discrepancy between
the underlying process and the fitted model was obtained from ARMA (2,1) model.
Hence, this model was considered as a better representative of the annual
rainfall values and was used to predict five years ahead values. The mean
absolute percentage error (MAPE) of the prediction was found to be less than
10%. Thus, ARMA (2,1) model could be used for forecasting and simulation of
annual rainfall for planning, management and design of water resources systems
in Debre Markos town.