Crisping the Fuzzy ARIMA Intervals of Possibility for Short Term Forecasts

The Fuzzy autoregressive integrated moving average (FARIMA) model is a fuzzy-enhanced version of the autoregressive integrated moving average (ARIMA) model that yield improved prediction accuracy with fewer data observations as compared to the classical ARIMA models. The FARIMA time series utilizes membership functions of the fuzzy coefficients and generates forecasts in the form of possibility intervals. However, the FARIMA model does not provide crisp forecast values for forecasting future possibility intervals. This paper aims to simultaneously achieve in-sample and out-sample intervals of possibility forecasts by converting Fuzzy ARIMA possibility intervals into crisp values. The method is tested on exchange rate of the New Taiwan Dollar (NTD) against the United States Dollar (USD) and the annual average mean surface air temperature of Nigeria. The results demonstrate that the proposed method produces out-of-sample possibility interval forecasts that closely align with those obtained using observed values in most cases. In addition, forecasts performance evaluation results indicate that the proposed method produces smaller MAPE and RMSE values in LB predictions while approximately competing in UB predictions compared to the considered methods in the literature. Moreover, the proposed method has advantage of forecasting future possibility intervals without relying on crisp out-of-sample observed values. This implies the method could aid policy makers in determining the worst and best projected bounds that could be used for making future decisions without actual out-of-sample crisp observations.