## 1 Introduction  
Time-series forecasting is commonly considered as a technique for estimating many future domains. It has become a major interest in statistical inference and predictions for researchers and academics [1]. Almost every aspect of life, including the economy [2], physics [3], agriculture [4], and engineering [5], has applied time-series analysis. In economics, the accurate forecasting of data from a financial time series allows investors to determine relevant strategies and techniques to reduce price risk and protect their investment from unacceptable loss. One of the most crucial applications of forecasting is in investment risk management. Thus, the scrupulous selection of an effective forecasting model is important for managing non-linearity to ensure critical input for plans and decisions. In a significant number of studies, generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) models have been used for time series forecasting, especially in estimating and predicting future values given the existence of ARCH effects in return series. Individual researchers can conveniently manipulate the GARCH and EWMA models as several resources are publicly available that can be used to develop forecasts effortlessly. [PERSON] [6] developed the GARCH model to estimate and predict future values given the existence of ARCH effects in return series in particular. The GARCH model has achieved significant success in describing in-sample forecasting characteristics [7]. Many studies used the GARCH model, for example, a study of the stochastic representation of impulsive noise in the frequency band [8], a study of the stock exchange market of China [9], and a study of Bitcoin volatility [10]. They found that the GARCH model is more accurate when compared to ordinary-least-square (OLS) and EWMA methods. From these studies, despite having publicly accessible tools to easily forecast data, the GARCH model performed better than the EWMA. Thus, our study used the GARCH model as a basis for improvement. Extensive research is being undertaken to improve the GARCH model by combining mathematical and statistical models, thus creating new models. For instance, a Glosten-Jagannathan-Runkle-GARCH (GJR-GARCH) model was introduced to allow for the conditional variance to respond to previous negative and positive changes differently [11], and was then applied in measuring extreme risks within a sustainable financial system [12]. A combination of an artificial neural network (ANN) and GARCH was proposed for the volatility forecasting of daily log-returns series in a study of international stock return volatility [13], and was then applied in a study of the Chinese energy market [14]. More improved GARCH models were introduced for variance-covariance and correlation forecasting, including the use of orthogonal components for displaying temporal aggregated properties that are not found when working with univariate models [15]; the use of copulas for conveniently linking univariate GARCH [16]; and the use of realized semi-variances, semi-covariances, and semi-correlations [17]. Most of the improved model was used for correlation components, such as covariances and volatilities of stock and bond returns [18; 19; 20; 21]. More extensive and complex GARCH models were developed to improve the forecasting model. For example, a fuzzy GJR-GARCH model using fuzzy inference systems [22], hybrid neural network GJR-GARCH models [23; 24] for volatility forecasting of indexes, a mixture of integer-valued models with different distributions in GARCH model [25], and a hidden Markov Exponential GARCH model for volatility forecasting of crude oil price [26]. Another approach toward improving the GARCH model was introduced by using a sliding window technique to forecast future values in various fields; this was called the sliding window GARCH (SWGARCH) model [27; 28]. These hybrid models produced more accurate results than the classic forecasting models considered in the studies.