Feature Extractions

Feature extraction is a crucial step in the process of analyzing and understanding complex data. In the context of financial markets, feature extraction involves identifying and extracting relevant information from large datasets to make informed decisions. In this article, we will explore various feature extraction techniques used in financial markets, including duration since last trade, mid price, EWMA price returns, order-weighted average price, spread, rolling spread mean, coefficient of variation, and z-score.

Duration since last trade

The duration since last trade is a feature that captures the time elapsed since the last trade occurred. This feature is useful in understanding the market's activity and can be used to identify periods of high or low activity.

$$\text{Duration since last trade} = \text{Current time} - \text{Time of last trade}$$

Mid price

The mid price is a feature that represents the average of the best bid and ask prices. This feature is useful in understanding the market's sentiment and can be used to identify periods of high or low volatility.

$$\text{Mid price} = \frac{\text{Best bid price} + \text{Best ask price}}{2}$$

EWMA Price Returns

EWMA (Exponentially Weighted Moving Average) price returns are a feature that mitigates tick sensitivity by computing returns using an exponentially weighted moving average of past prices. This feature is useful in understanding the market's trend and can be used to identify periods of high or low volatility.

$$r_t^{(T)} = \log \left( \frac{P_t}{\text{EWMA} \left(P, \lambda = \frac{1}{T} \right)} \right)$$

Order-weighted average price

The order-weighted average price is a feature that represents the weighted average of the best bid and ask prices. This feature is useful in understanding the market's sentiment and can be used to identify periods of high or low volatility.

$$OWA = \frac{\sqrt{\text{ask size}}}{\sqrt{\text{ask size} + \text{bid size}}} \times \text{best bid price} + \frac{\sqrt{\text{bid size}}}{\sqrt{\text{ask size} + \text{bid size}}} \times \text{best ask price}$$

Spread

The spread is a feature that represents the difference between the best ask and bid prices. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{Spread} = \text{best ask price} - \text{best bid price}$$

Rolling Spread Mean, Coefficient of Variation & Z-score

The rolling spread mean, coefficient of variation, and z-score are features that track the mean, coefficient of variation, and z-score of the spread over a given rolling time period. These features are useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{Spread Mean}_t = \frac{1}{T} \sum_{i=t-T}^{t} \text{Spread}_i$$

$$\text{Spread CV}_t = \frac{\text{Spread Std}_t}{\text{Spread Mean}_t}$$

$$\text{Spread Z-score}_t = \frac{\text{Spread}_t - \text{Spread Mean}_t}{\text{Spread Std}_t}$$

$$\frac{\text{Spread Std}_t} = \sqrt{\frac{1}{T} \sum_{i=t-T}^{t} (\text{Spread}_i - \text{Spread Mean}_t)^2}$$

Trade direction (sign)

The trade direction (sign) is a feature that marks trades with +1 for buyer-initiated and -1 for seller-initiated. This feature is useful in understanding the market's sentiment and can be used to identify periods of high or low volatility.

Size imbalance

The size imbalance is a feature that represents the absolute difference between the number of shares at the bid and ask. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{SI} = \frac{\text{ask size} - \text{bid size}}{\text{ask size} + \text{bid size}}$$

Order imbalance

The order imbalance is a feature that represents the absolute difference between the volume of buyer-initiated and seller-initiated trades, divided by their sum over a fixed volume bucket. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{I}_n = \frac{\left| V_n^B - V_n^S \right|}{V_n^B + V_n^S}$$

Volume-weighted probability of informed trading (VPIN)

The volume-weighted probability of informed trading (VPIN) is a feature that represents the rolling average of order imbalance over the last N volume buckets. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$VPIN = \frac{1}{N} \sum_{n=1}^{N} I_n$$

Trade Flow

The trade flow is a feature that represents the running tally of signed trade sizes where the sign is defined as 1 if the trade was seller-initiated and -1 if it was buyer-initiated. This feature is useful in understanding the market's sentiment and can be used to identify periods of high or low volatility.

$$F_t^{(\tau)} = V_{(t-\tau, t)}^B - V_{(t-\tau, t)}^S$$

Order Flow Imbalance (OFI)

The order flow imbalance (OFI) is a feature that represents the changes in supply and demand at the best bid and ask prices. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{OFI} = (\text{Best Bid Size}_{t} - \text{Best Bid Size}_{t-1}) - (\text{Best Ask Size}_{t} - \text{Best Ask Size}_{t-1})$$

Market Pressure (MP)

The market pressure (MP) is a feature that captures the aggressiveness of market orders relative to available liquidity. This feature is useful in understanding the market's liquidity and can be used to identify periods of high or low liquidity.

$$\text{MP}_t = \frac{\text{Trade Volume}_t}{\text{Bid Size}_t + \text{Ask Size}_t}$$

In conclusion, feature extraction is a crucial step in the process of analyzing and understanding complex data. The features discussed in this article are useful in understanding the market's liquidity, sentiment, and volatility. By extracting these features, traders and investors can make informed decisions and gain a competitive edge in the market.

Future Work

Future work can involve exploring other feature extraction techniques, such as:

• Using machine learning algorithms to identify patterns in the data
• Incorporating external data sources, such as economic indicators and news articles
• Developing more sophisticated models to predict market behavior

By continuing to develop and refine feature extraction techniques, we can gain a deeper understanding of the market and make more informed decisions.

References

• [1] "Feature Extraction for Financial Markets" by [Author]
• [2] "Machine Learning for Financial Markets" by [Author]
• [3] "Feature Extraction for Time Series Data" by [Author]

Code

The code for the feature extraction techniques discussed in this article can be found in the following repository:

• [Repository URL]

Note: The code is written in Python and uses the pandas and numpy libraries.

Conclusion

Feature extraction is a crucial step in the process of analyzing and understanding complex data. The features discussed in this article are useful in understanding the market's liquidity, sentiment, and volatility. By extracting these features, traders and investors can make informed decisions and gain a competitive edge in the market. Future work can involve exploring other feature extraction techniques and developing more sophisticated models to predict market behavior.

In our previous article, we discussed various feature extraction techniques used in financial markets, including duration since last trade, mid price, EWMA price returns, order-weighted average price, spread, rolling spread mean, coefficient of variation, and z-score. In this article, we will answer some frequently asked questions about feature extraction in financial markets.

Q: What is feature extraction in financial markets?

A: Feature extraction is the process of identifying and extracting relevant information from large datasets to make informed decisions. In financial markets, feature extraction involves identifying and extracting features that can help traders and investors understand market behavior and make predictions about future market movements.

Q: Why is feature extraction important in financial markets?

A: Feature extraction is important in financial markets because it allows traders and investors to identify patterns and trends in market data that can help them make informed decisions. By extracting relevant features from market data, traders and investors can gain a competitive edge in the market and make more profitable trades.

Q: What are some common feature extraction techniques used in financial markets?

A: Some common feature extraction techniques used in financial markets include:

• Duration since last trade
• Mid price
• EWMA price returns
• Order-weighted average price
• Spread
• Rolling spread mean, coefficient of variation, and z-score
• Trade direction (sign)
• Size imbalance
• Order imbalance
• Volume-weighted probability of informed trading (VPIN)
• Trade flow
• Order flow imbalance (OFI)
• Market pressure (MP)

Q: How do I choose the right feature extraction technique for my needs?

A: Choosing the right feature extraction technique depends on your specific needs and goals. You should consider the type of data you are working with, the type of analysis you want to perform, and the level of complexity you are comfortable with. It's also a good idea to experiment with different techniques to see which one works best for you.

Q: Can I use machine learning algorithms to improve feature extraction?

A: Yes, you can use machine learning algorithms to improve feature extraction. Machine learning algorithms can be used to identify patterns and relationships in data that may not be apparent through traditional feature extraction techniques. However, machine learning algorithms require large amounts of data and computational resources, so they may not be suitable for all applications.

Q: How do I evaluate the performance of a feature extraction technique?

A: Evaluating the performance of a feature extraction technique involves comparing the results of the technique to a baseline or benchmark. You can use metrics such as accuracy, precision, recall, and F1 score to evaluate the performance of a feature extraction technique.

Q: Can I use feature extraction techniques to predict market behavior?

A: Yes, you can use feature extraction techniques to predict market behavior. By extracting relevant features from market data, you can identify patterns and trends that can help you make predictions about future market movements.

Q: What are some common challenges associated with feature extraction in financial markets?

A: Some common challenges associated with feature extraction in financial markets include:

• Handling high-dimensional data
• Dealing with missing or noisy data
• Selecting the right feature extraction technique
• Evaluating the performance of a feature extraction technique
• Handling non-stationarity in data

Q: How can I overcome these challenges?

A: You can overcome these challenges by:

• Using dimensionality reduction techniques to reduce the number of features
• Using imputation techniques to handle missing data
• Using robust feature extraction techniques that can handle noisy data
• Using cross-validation to evaluate the performance of a feature extraction technique
• Using techniques such as wavelet analysis to handle non-stationarity in data

Q: What are some best practices for feature extraction in financial markets?

A: Some best practices for feature extraction in financial markets include:

• Using a combination of feature extraction techniques to get a more complete picture of market behavior
• Using robust feature extraction techniques that can handle noisy data
• Using techniques such as cross-validation to evaluate the performance of a feature extraction technique
• Using techniques such as dimensionality reduction to reduce the number of features
• Using techniques such as imputation to handle missing data

By following these best practices and overcoming the challenges associated with feature extraction, you can use feature extraction techniques to gain a competitive edge in the market and make more profitable trades.