## 1 Introduction
Although these numerical models outperform the conventional forecasting models, forecasting errors are still debated regarding the issue of accuracy. Forecasting accurately facilitates researchers in decision-making; therefore, the existing models must be improved. The applications of ANN, GJR, and Markov chain methods are very popular but undesirable in this study due to their complex and lengthy computation processes. The computation is also not easy to understand and only concerned with weight adjustment [29]. Moreover, the common neural networks are inefficient for detecting nonlinear or dynamic behaviors [30] and are unable to independently manage data uncertainties [31], thus decreasing the forecasting efficiency. It is important to develop a new forecasting model with a low accuracy error [32]. In addition, the fuzzy theory in some hybrid models [33; 34] can estimate nonlinear continuous functions uniformly with an arbitrary accuracy, thereby producing more precise results than GARCH models. However, the computations of the hybrid fuzzy models are lengthy and incomprehensible. Thus, our study considers improving the GARCH model into a more understandable and less complex model. In previous studies, the GARCH models were sensitive to extreme values in certain seasonal months [14; 27]. The sensitivity of the GARCH model depends on the parameter estimation using the maximum likelihood method (MLM). The likelihood method is sensitive to the selection of initial values and the data distribution. The existence of uncertainties in time-series data makes it unreliable to employ the likelihood method to manage the uncertainties because no specific distribution is known. This drawback poses a major issue in terms of the instability of time-series forecasting. The GARCH model imposes parameter restrictions that are often violated by estimated coefficientsthat may improperly limit the dynamics of the conditional variance process [35]. The GARCH model is also unable to capture the influence of each variance in the observation as the model uses a long-run average variance. The calculation of the long-run average variance, which is used to determine the weight of forecast, only considers the series in its entirety; therefore, the information on different effects of the variances in each observation is disregarded. Hence, our study improves the GARCH model in terms of parameter estimation and variance calculation to search for the most effective model for forecasting time-series data. Therefore, this study proposes a new time-series forecasting model by combining the GARCH model with two methods; the first model is the fuzzy linear regression (FLR), which is used to estimate the parameters of the model, and the second is the fuzzy sliding window (FSW) variance, which is used to determine the weight of the forecast. The FLR is used for parameter estimation to reduce the computation risk and overcome the inter-correlation problem associated with independent variables [36]. It is capable of addressing uncertainties and handling fluctuating information and/or linguistic variables. The FLR is also more robust at handling outlier effects [37]. When applied to finance, FLR generates better estimates than the traditional approach [38]. This approach is very useful when facing unstable time-series data caused by uncertainties. The FSW variance is used to calculate the variance of the model. The FSW variance improves the proposed model by replacing the component of the long-run average variance in the GARCH. The FSW variance combines fuzzy theory and the sliding window technique. Applications of the sliding window technique are useful in forecasting [39]. The technique was used to determine the adjustment weights of the forecast and a certain number of splits to create a small number of intervals [40]. The performance of the sliding window technique enables researchers to understand how cases work and change the efficiency pattern [41].