The Use of Fractionally Autoregressive Integrated Moving Average for the Rainfall Forecasting

Abstract

A study of rainfall pattern and its variability in South Asian countries is vital as those regions are frequently vulnerable to climate change. Models for rainfall have been developed with different degrees of accuracy, since this key climatic variable is of importance at local and global level. This study investigates the rainfall behaviour using the long memory approach. Since the observed series consists of an unbounded spectral density at zero frequency, a fractionally integrated auto regressive model (ARFIMA) is fitted to explore the pattern and characteristics of the weekly rainfall in the city of Colombo. The maximum likelihood estimation (MLE) method was utilized to obtain estimates for model parameters. To evaluate the suitability of the method for parameter estimation, a Monte Carlo simulation was done with various fractionally differenced parameter values. Model selection was done based on the minimum of the mean absolute error and validated by the forecasting performance that was evaluated using an independent sample. The experimental result yielded a good prediction accuracy with a best fitted long range dependency model and a coverage probability of 95% in terms of prediction intervals that resulted in closer nominal coverage.