# Demand Forecasting in Supply Chain Using Uni-Regression Deep Approximate Forecasting Model
## 3 Proposed Methodology
### Feature Extraction
#### 3.3.3 Time Series Features  
The joint use of these time series feature extraction methods is substantially supportive in the identification of time-dependent trends critical for forecasting within the dynamic supply chain environment. Each method provides a specific angle of view and helps to understand demand dynamics better. The use of simple averages, logarithmic transformations, weighted averages, and multi-level linear modeling in their analysis means that it becomes more reliable, allowing forecasting models to capture as well as adapt temporal patterns hidden within supply chain data.  
The simple mean is a basic method that computes the arithmetic average of given values. In the framework of time series analysis, it constitutes a mean line by smoothing away short-term variations and accentuating long-run tendencies. The average is fundamental in detecting the general direction of demand attaining over time, which helps establish a permanent base point for detecting broader patterns and trends as well as reducing fluctuations due to short-term effects.  
\[SA=\frac{1}{n}\underline{\sum_{f=1}^{n}S_{i}^{*}} \tag{8}\]  
Log-log linear regression uses logarithmic transforms of the data. This method will allow for a qualitative evaluation and quantification of the rate at which change occurs over time, by converting data to a log-log scale. One of the advantages of log-log linear regression is that it helps in identifying exponential or power law relationships within time series data. It reveals how the demand dynamics change over time and allows more accurate modeling of nonlinear trends.  
\[\log(x)=e.\log(y)+c \tag{9}\]  
In this case, \(\log(x)\) is the dependent variable while \(\log(y)\) is the independent variable, with \(e\) being the slope and \(c\) the intercept.  
Weighted average assigns weighting based on the importance of data points. This implies that outliers can exist such that some data points have a greater effect on the average calculation than others, indicating their prominence in analysis. The weighted average gives more significance to important points of data so that changing patterns can be captured accurately. This is especially useful when some periods or events are more important for prediction.  
\[WA=\frac{\sum_{f=1}^{n}w_{f}.S_{i}^{*}}{\sum_{f=1}^{n}w_{f}} \tag{10}\]  
(d) Two-level Linear Model  
Two-level linear model techniques refer to the use of two-level applications of linear modeling for the analysis of complex relationships in data. This might involve hierarchical or multi-layered modeling, where notions of different levels are regarded at the same time. Two-level linear model methods provide a powerful framework for modeling complex structures and hierarchies in time series data. Through the study of interdependences at different levels, these approaches contribute to a better understanding of factors affecting demand habits over time.  
\[x=\alpha_{0}+\alpha_{1}.T_{11}^{*}+\alpha_{2}.T_{12}^{*}+\ldots+\in \tag{11}\]  
Here, \(x\) is the dependent variable whereas \(T_{11}^{*}\) and \(T_{12}^{*}\) are independent variables at various levels, while \(\alpha_{0},~{}\alpha_{1},~{}\alpha_{2}\) denote coefficients and \(\in\) is referred to as the error term.