## 3 Multi-Dimensional Fusion Feature-Enhanced Prediction Method
### Data Augmentation of Multi-Dimensional Feature Engineering
#### 3.1.2 Fluctuation Index  
Volatility indicators are mainly used to measure the intensity of price fluctuations, which helps to capture market uncertainties and risk factors, thus providing a more comprehensive perspective for price forecasting.  
(1) Rate of return  
The rate of return evaluates the change in price by determining the percentage shift in the closing value (\(Returns\)). The formula for this calculation is as follows:  
\[Returns_{t}=\frac{P_{t}-P_{t-1}}{P_{t-1}}. \tag{4}\]  
Here, \(P_{t}\) denotes the closing price for the current period, while \(P_{t-1}\) signifies the closing price from the prior period. The return rate effectively captures the extent of price fluctuations and serves as a key metric for assessing short-term market instability. Through examining the dispersion and direction of these returns, we can gain insights into market dynamics and the pace at which prices are shifting.  
(2) Volatility  
Volatility is determined through the standard deviation of the return rate, employing a sliding window of 20 periods. The formula for this calculation is as follows:  
\[Volatility_{t}=\sqrt{\frac{\sum_{i=t-19}^{t}\bigl{(}Returns_{i}-\overline{Returns }\bigr{)}^{2}}{20}}. \tag{5}\]  
Among these, \(Returns_{i}\) represents the return rate over the i period, while \(Returns\) signifies the mean return rate within a sliding window. Volatility measures the consistency of price movements. Increased volatility implies higher market risk and more drastic price shifts. Conversely, decreased volatility suggests a more stable market. In the realm of financial risk management, volatility serves as a crucial metric for gauging asset risk. For predicting futures prices, variations in volatility can offer insights into the potential range and direction of future price movements.  
(3) Amplitude  
The amplitude is determined by computing the ratio of the gap between the day's peak price and its lowest point to the opening value. The formula for this calculation is as follows:  
\[Amplitude_{t}=\frac{High_{t}-Low_{t}}{Open_{t}}. \tag{6}\]  
In this context, \(High_{t}\) signifies the peak price of the day, \(Low_{t}\) denotes the lowest price recorded, and \(Open_{t}\) stands for the initial price at the market's opening. The amplitude serves as a direct indicator of the extent of price variations throughout the day. A more pronounced amplitude suggests significant disparities in prices and heightened trading activity, potentially signaling a shift in the overall market trend or an increase in short-term volatility.  
(4) Price interval characteristics  
Determine the gap between the maximum and minimum prices (price range) as a feature, with the formula succinctly given by the following:  
\[PriceRange_{t}=High_{t}-Low_{t}. \tag{7}\]  
This aspect resembles amplitude, but zeroes in on the absolute span of price fluctuations, thereby enhancing the volatility measure. It offers a multifaceted view of price variability and supplies additional volatility data for the predictive model.  
(5) Trading volume changes  
Determine the percentage shift in volume (volume change) using the following formula:  
\[VolumeChange_{t}=\frac{Volume_{t}-Volume_{t-1}}{Volume_{t-1}}. \tag{8}\]  
Here, \(Volume_{t}\) signifies the present trading volume, while \(Volume_{t-1}\) stands for the prior trading volume. Often, a relationship exists between the alteration in trading volume and price movement. For instance, during a price increase, a consistent rise in trading volume might suggest robust bullish momentum, indicating a likely continuation of the upward trend; conversely, if trading volume surges during a price drop, it could signal that bearish forces are in control, potentially leading to a more pronounced downward trend.