A Novel Fuzzy Linear Regression Sliding Window GARCH Model for Time-Series Forecasting

Abstract

Generalized autoregressive conditional heteroskedasticity (GARCH) is one of the most popular models for time-series forecasting. The GARCH model uses a maximum likelihood method for parameter estimation. For the likelihood method to work, there should be a known and specific distribution. However, due to uncertainties in time-series data, a specific distribution is indeterminable. The GARCH model is also unable to capture the influence of each variance in the observation because the calculation of the long-run average variance only considers the series in its entirety, hence the information on different effects of the variances in each observation is disregarded. Therefore, in this study, a novel forecasting model dubbed a fuzzy linear regression sliding window GARCH (FLR-FSWGARCH) model was proposed; a fuzzy linear regression was combined in GARCH to estimate parameters and a fuzzy sliding window variance was developed to estimate the weight of a forecast. The proposed model promotes consistency and symmetry in the parameter estimation and forecasting, which in turn increases the accuracy of forecasts. Two datasets were used for evaluation purposes and the result of the proposed model produced forecasts that were almost similar to the actual data and outperformed existing models. The proposed model was significantly fitted and reliable for time-series forecasting.