## 3 Proposed Methodology for Out-of-Stock Prediction Model Using BCHO-TCN LightGBM
### Feature Extraction  
The main objective of feature extraction is to recognize important traits within the input data. This study utilizes the following techniques to extract features.  
In general, statistical characteristics are features such as summary statistics derived from the dataset that describe its distribution, central tendency, variability, and shape. These elements offer information about the hidden patterns and features of the data, which can add value to predictive modeling. Common statistical features include the following:  
1. Mean: The first raw moment that informs about average stock levels during the period under consideration is a mean. The mean is defined as \[M=\frac{1}{N}{\sum_{r=1}^{N}{K_{r}^{*}}}\] (2) Here, the preprocessed data point present in the dataset is denoted as \(K_{r}^{*}\), and the overall number of preprocessed data points is denoted as \(N\).
2. Variance: Variance can be described as the square of the difference between a random variable and its average value in arithmetic terms. In Equation (3), the variance formula itself is given. \[\sigma^{2}=\frac{1}{N}{\sum_{r=1}^{N}{(K_{r}^{*}-M)}^{2}}\] (3)
3. Standard deviation: The standard deviation defines the spread or variability of the levels of the stock surrounding the mean value. A greater value of standard deviation demonstrates larger fluctuations, which signifies variations in stock supply over time. \[\sigma=\sqrt{\sigma^{2}}\] (4)* Skewness: This is a statistical concept that measures the asymmetry of a probability distribution of a random variable compared to its mean. In the field of probability theory and statistics, the skew of returns may be positive, zero, negative, or undetermined. \[SK=\frac{\frac{1}{N}\underline{\sum_{r=1}^{N}}(K_{r}^{*}-M)^{3}}{\sigma^{3}}\] (5)
* Kurtosis: This is a mathematical computation that shows that the temporal tails of a distribution go further than the ones of nominal distribution. This implies that kurtosis is a measure of the extremes in the tails of a given distribution. \[KU=\frac{\frac{1}{N}\underline{\sum_{r=1}^{N}}(K_{r}^{*}-M)^{4}}{\sigma^{4}}\] (6)
* Entropy: Entropy quantity is used to measure the level of disorder in a random variable. This implies that higher entropy values tend to occur in the presence of greater unpredictability in stock behavior. \[E_{n}=-\underline{\sum_{r=1}^{N}}p(K_{r}^{*})\log_{2}(p(K_{r}^{*}))\] (7) Here, in the preprocessed dataset, the probability occurrence of each unique value is denoted as \(p(K_{r}^{*})\).
* Min and max: This feature shows us the maximum and minimum inventory levels of this dataset. They provide information concerning stock levels and assist in the comprehension of the best upper and lower bounds of stock availability. \[\min=\min(K^{*}\;_{1},K^{*}\;_{2},.......K^{*}\;_{N})\] (8) \[\max=\max(K^{*}\;_{1},K^{*}\;_{2},.......K^{*}\;_{N})\] (9)
* Sum: Stock is presented as a sum of stock levels over a period of time. This provides an overview of stock availability in a given time span, and allows for the analysis of trends. \[S=\sum_{r=1}^{N}K_{r}^{*}\] (10) The final statistical feature output is denoted as s.