## 2 Methods
### Technical Details
#### 2.4.1 Methods for Forecasting  
Different statistical and data-driven methodologies are investigated in this study to evaluate a reliable forecast framework to evaluate their performance. There are respective impacts on the business from both a managerial and mathematical perspective. The selection of the forecasting methods we tested are categorized as: (i) statistical (e.g., Simple Exponential Smoothing (SES), Autoregressive Integrated Moving Average (ARIMA)); (ii) artificial intelligence (e.g., RF, SVR, W-ANN, W-LSTM). When we use a data-driven approach, we divide the data set into an 80:20 ratio to consider as a training and test set. All the forecasting methods are implemented and written in Python programming language. A brief description of each of these methods is presented below:  
Simple Exponential Smoothing (SES): Simple exponential smoothing is a method that considers the previous observation in a data set and forecasts the next value by  
Figure 1: Evaluation procedure. a predetermined smoothing constant \(\alpha\), typically between 0 and 1, which is added to the difference between the past value and the next. This error gap between the past and next observations and the simplicity of the model is the main driver for its piratical implementation. The smoothing constant used in our study is optimized automatically. SES is easy to learn and apply and only requires a small sample of historical data. However, the disadvantage is that the model is inaccurate for long-term forecasts and is negatively affected by volatile demand [28]. Autoregressive Integrated Moving Average (ARIMA): Autoregression integrated moving average is a statistical forecast model that seeks to capture correlations between observations in a time series data set. ARIMA can be understood by describing its components: (i) Autoregression (AR), (ii) Integrated (I), and (iii) Moving Average (MA). The **(AR)** uses observations from past time steps as input to the regression. The parameter \(p\) specifies the number of past time steps used. **(I)** is the differentiation of the original observations, which transforms non-stationary data into stationary. The parameter \(d\) specifies how many orders of difference are considered to be differentiated to become stationary. **(MA)** establishes autocorrelation between observations and outputs a residual error to lagged observations. The parameter q determines the number of moving averages included in the model [30]. To determine the order of the ARIMA(p,d,q) models in this paper, the Akaike Information Criterion (AIC) has been used. The ARIMA model has the advantages of capturing trends and seasonality, however, but fails to capture intrinsic non-linearity [31]. Support Vector Regression (SVR): SVR is a classical approach based on statistical learning theory. The method is based on the principle of identifying a function that minimizes risk in opposite to finding empirical errors like in linear regression [32; 33]. Three hyper-parameters govern the performance of a given SVR model. The parameters are determined either through theoretical error bounds or experimentation of error by cross-validation. However, in practical cases, parameter tuning is difficult, based on the complex nature of the parameter space. This means it can be challenging to determine the relationship between the parameter and the input noise [34; 35; 33]. We identified SVR key advantages by the model's ability to comprehend small data sets that consist of non-stationary and volatile data. Random Forest (RF): Random Forest is an algorithm within machine learning, which can be used for both classification and regression. RF has the ability to serve as a method for a wide range of predictive problems especially within piratical problems [36]. RF is a method that has the advantage of being able to handle the data of both relatively small samples as well as large-scale complex data structures. The model simplicity make it easy to use and the model consists of few parameters [37; 38].