Machine Learning and Deep Learning Algorithm Trading, Preprocessing Methods for Noisy Data Using Wavelets

In the field of data science, various methodologies are used, and machine learning and deep learning technologies are especially utilized in the development of automated trading systems in the financial sector. These systems must extract meaningful patterns from noisy data, making data preprocessing essential. In this course, we will have an in-depth discussion on approaches to preprocessing noisy data using wavelet transforms.

1. Basics of Machine Learning and Deep Learning

Machine learning deals with algorithms that learn and predict automatically through data, while deep learning is a subset of machine learning based on neural network structures. Considering the complexity and volatility of financial markets, these technologies can greatly assist in the development of predictive models.

1.1 Machine Learning Techniques

The main techniques of machine learning are as follows:

  • Regression Analysis: Used to predict continuous values.
  • Classification: Useful for determining whether given data belongs to a specific category.
  • Clustering: Groups data points based on similarity.
  • Reinforcement Learning: Learns strategies to maximize rewards through the interaction of an agent with its environment.

1.2 Deep Learning Techniques

The main techniques of deep learning are as follows:

  • Artificial Neural Networks (ANN): Composed of input layers, hidden layers, and output layers.
  • Convolutional Neural Networks (CNN): Mainly used for image analysis.
  • Recurrent Neural Networks (RNN): Strong in processing time series data.

2. Importance of Data Preprocessing

Data preprocessing is a crucial step in maximizing the performance of machine learning models. Raw data is often noisy and may contain missing values or outliers, which can negatively affect the learning process of the model. Therefore, it is necessary to refine and transform the data into a suitable form for learning.

3. What is Noisy Data?

Noisy data contains randomness that interferes with data analysis. In financial markets, price fluctuation data can inherently include noise, which can adversely affect the accuracy of predictive models. Such noisy data often arises from the following causes:

  • Volatility of market psychology
  • Unexpected news events
  • Sudden increases or decreases in trading volume

4. Wavelet Transform

The wavelet transform is a method that separates signals into various frequency components, tracking changes across all time domains. This allows for the analysis of signals across different frequency bands. The advantages of wavelet transform are as follows:

  • Multi-level Analysis: Can capture volatility occurring in specific parts of the signal.
  • Local Feature Capture: Useful for filtering noise in specific time intervals.
  • Non-linear Signal Processing: Strong in processing data with non-linearity.

4.1 Types of Wavelet Transforms

The primary types of wavelet transforms are as follows:

  • Haar Wavelet: The simplest form of wavelet, fast and simple but may have lower resolution.
  • Daubechies Wavelet: Suitable for smooth signals and allows for various parameters to be set.
  • Meyer Wavelet: Smoothly connects changes at different frequencies.

5. Procedure for Preprocessing Noisy Data Using Wavelets

The procedure for preprocessing noisy data using wavelet transforms is as follows:

  1. Raw Data Collection: Collect various data such as financial data, prices, and transaction volumes.
  2. Apply Wavelet Transform: Use the selected wavelet transform to convert the data.
  3. Noise Removal: Filter out noise by removing specific frequency components.
  4. Inverse Wavelet Transform: Restore the filtered signal to output the final data.

5.1 Sample Code

Below is an example of applying wavelet transform using the PyWavelets library in Python:

import pywt
import numpy as np

# Generate raw data (e.g., stock price data)
data = np.random.rand(512) 

# Perform wavelet transform (using Daubechies Wavelet)
coeffs = pywt.wavedec(data, 'db1')
threshold = 0.1

# Remove noise
coeffs_filtered = [pywt.threshold(c, threshold) for c in coeffs]

# Inverse wavelet transform
data_filtered = pywt.waverec(coeffs_filtered, 'db1')

6. Model Training and Evaluation

Based on the noise-free data obtained by wavelet transforms, machine learning and deep learning models can be built. The typical model training process is as follows:

  1. Data Splitting: Divide into training data and test data to prevent overfitting.
  2. Model Selection: Experiment with various models such as Random Forest, XGBoost, and LSTM.
  3. Model Training: Train the model using the training data.
  4. Model Evaluation: Evaluate the model’s performance using the test data.

6.1 Model Evaluation Metrics

Common metrics for evaluating model performance are as follows:

  • Accuracy: The proportion of correctly predicted instances out of the total samples.
  • Precision: The proportion of actual positive samples among the predicted positive samples.
  • Recall: The proportion of correctly predicted instances out of the actual positive samples.

7. Conclusion

Algorithmic trading using machine learning and deep learning can be powerful tools; however, neglecting the preprocessing of noisy data can significantly degrade performance. Wavelet transform is an effective method for noise removal, offering the advantage of analyzing signals across various frequency bands. Therefore, through proper preprocessing steps, more reliable trading strategies can be developed.

8. References

The following are the main references used in this course:

  • Wavelet Theory and Applications, 2010
  • Machine Learning for Trading, 2016
  • Deep Learning for Time Series Forecasting, 2019