## 2 Literature Review  
Because of the broad nature of time series forecasting, the literature review is confined to previous works related directly to our proposed approach. The subject of hybridization, which covers umbrella structures combining different forecasting methods, can be divided into two broad categories. In the first category, each model runs independently and generates a separate forecast. These forecasts are then consolidated into a final number. The pioneering work of [PERSON] and [PERSON] [2] falls into this category. Their method involves generating two separate forecasts and then averaging them into a single number. In the second category, models are connected in series. Figure 1 shows a simple, serially connected model, where the output of the first model is directly fed into the second one. In this serial combination, the underlying implicit assumption is that the series can be decomposed into distinct sub-categories. Once the series is decomposed, we can handle each sub-category with a different model. For the serial combination of models, the earliest arrangement is proposed by [PERSON] [5], where ARIMA (autoregressive integrated moving average) and ANN are connected in  
Figure 1: A serially connected hybrid model. series as basic and secondary models. Following this work, various serially connected models utilizing both linear and nonlinear methods have been proposed. Additionally, the original approach was fine-tuned for better performance [6]. The accumulated work on serially connected hybrid models can be further divided into two broad categories. The first category includes studies that propose a new forecasting method for basic or secondary models. The \"new\" methodology does not necessarily refer to an original approach, but it is something new within the context of serial hybridization. Here, the emphasis is on the novelty of the method used, and model verification and validation are often done by using popular data sets from the literature. The second category of research is about applications of hybrid models. This work aims to generate the most accurate forecast and often involves trial and error with multiple hybrid alternatives. One caveat is that the categorization schema presented above is not clear-cut, and some works can claim novelty in terms of both methodology and the data sets involved. Within the framework of this broad division, the list of recent works for each category is listed below. For methodology-oriented research: autoregressive moving average (MARMA) and exogenous multi-variable input [7], ARIMAX (ARIMA with explanatory variables), Holt-winters, ANN [8], SARIMAX (seasonal ARIMA with explanatory variables), LSSVM (least-squares support-vector machine) [9], ARMAX, ANN [10], ARIMA and ANN [11; 12; 13], ARIMA and GNN (granular neural networks) [14]. For application-oriented research: wind speed forecasting [8; 15], oil prices [12], tourist arrivals [16], monthly rainfall [9], computer network traffic [17], dengue epidemics [12], electricity consumption [18], power plant fuel consumption [19], stock market [20], and urban water demand [21]. Two interesting serial-model studies deserve special mention, as they are directly related to our work. In both studies, the output of the first model is not sent directly to the secondary model. Instead, the residuals, the difference between actual and fitted values, are analyzed and then sent to the second model according to a preset algorithm. The first approach proposed by [PERSON] et al. [6] combines ARIMA with PNN (probabilistic neural networks) as the first and secondary models. The PNN utilizes the error output of the ARIMA. Error values coming out of ARIMA are categorized, and each category is treated differently by PNN. The second study, by [PERSON] and [PERSON] [22], also uses the ARIMA and ANN combination, and it has a similar error classification mechanism between the first and second models. The error output of the first model is classified according to the spread around the mean.