Abstract
Most frequently used models for modeling and forecasting periodic climatic time series do not have the capability of handling periodic variability that characterizes it. In this paper, the Fourier Autoregressive model with abilities to analyze periodic variability is implemented. From the results, FAR(1), FAR(2) and FAR(2) models were chosen based on Periodic Autocorrelation function (PeACF) and Periodic Partial Autocorrelation function (PePACF). The coefficients of the tentative model were estimated using a Discrete Fourier transform estimation method. FAR(1) models were chosen as the optimal model based on the smallest values of Periodic Akaike (PAIC) and Bayesian Information criteria (PBIC). The residual of the fitted models was diagnosed to be white noise. The in-sample forecast showed a close reflection of the original rainfall series while the out-sample forecast exhibited a continuous periodic forecast from January 2019 to December 2020 with relatively small values of Periodic Root Mean Square Error (PRMSE), Periodic Mean Absolute Error (PMAE) and Periodic Mean Absolute Percentage Error (PMAPE). The comparison of FAR(1) model forecast with AR(3), ARMA(2,1), ARIMA(2,1,1) and SARIMA( 1,1,1)(1,1,1)12 model forecast indicated that FAR(1) outperformed the other models as it exhibited a continuous periodic forecast. The continuous monthly periodic rainfall forecast indicated that there will be rapid climate change in Nigeria in the coming yearly and Nigerian Government needs to put in place plans to curtail its effects.
Highlights
Understanding the variability in climatic time series data of a region over a long period gives one an idea about the climate change of such region [1]
Fourier Autoregressive (FAR)(1) models estimation is given in equation (12) were chosen as the optimal models based on the smallest values of Periodic Akaike (PAIC) and Bayesian Information criteria (PBIC) given in table 1
AR(3), Autoregressive Moving Average (ARMA)(2,1) and Autoregressive Integrated Moving Average (ARIMA)(2,1,1) models are not appropriate for forecasting Nigerian rainfall since the forecast values from these models did not reflect the seasonality and periodicity that is usually present in rainfall series
Summary
Understanding the variability in climatic time series data of a region over a long period gives one an idea about the climate change of such region [1]. The change in the measures of climatic variables has been attributed to natural and man-made reasons [2]. Based on the growing consensus among several scientific kinds of literature that in the coming decades, there will be a rapid increase in climatic time series variability level worldwide. This will be unfavourable for crop growth and yields in many regions and countries [4,5,6]. Nigeria like other countries in sub-Saharan Africa is highly vulnerable to the impacts of climate change [9]
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