Statistical Modeling and Prediction of Rainfall Time Series Data.
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Date
2014-07
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Publisher
Journal of the Nigerian Association of Mathematical Physics
Abstract
Climate and rainfall are highly non-linear and complicated phenomena, which requires classical , modern and detailed models to obtain accurate prediction. In this paper, we present tools for modelling and predicting the behavioural pattern in rainfall phenomena based on past observations. The paper introduces three fundamentally different approaches for designing a model , the statistical method based on autoregressive Integrated Moving Average(ARIMA), the emerging fuzzy time series(FTS) model and non-parametric method(Theil's regression). In order to evaluate prediction efficiency, we made use of 31 years annual rainfall data from year 1982 to 2012 of Ibadan, Oyo state, Nigeria. The Fuzzy time series model has its universe of discourse divided into 13 intervals and the interval with the largest number of rainfall data is divided into 4 sub intervals of equal length. Three rules were used to determine if the forecast value under FTS is upward 0.75 -point, middle or downward 0.25-point. ARIMA(1,2,1) was used to derive the weights and the regression coefficients, while the Theil's regression was used to fit a linear model. The performance of the model was evaluated using mean squared forecast error(MAE) and root mean square forecast error (RMSE) and coefficient of determination. The study reveals that FTS model can be used as an appropriate forecasting tool to predict the rainfall, since it outperformed the ARIMA and Theil's models.
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Keywords
Fuzzy time series, Autoregressive integrated moving average, Theil's regression, Root mean square forecast error, Mean squared forecast error, Coefficient of determination