the_information_nexus/financial_docs/ml_trading.md

Technical Guide for Forex Time Series Analysis Using AI/ML Models

Objective

This guide provides a comprehensive overview of the methodologies and machine learning models used in analyzing forex time series data, focusing on EUR/USD and other major and minor pairs. The goal is to understand the underlying technical principles, implement feature engineering, perform correlation analysis, identify trends, train AI/ML models, and evaluate their performance using RMSE.

Key Components

1. Data Preparation
2. Feature Engineering
3. Correlation Analysis
4. Trend Identification
5. Model Training
6. Model Evaluation

1. Data Preparation

Context

Forex data is high-frequency time series data that requires careful preprocessing to handle missing values, outliers, and ensure consistency. TimescaleDB is used for efficient storage and retrieval due to its scalability and time-series optimizations.

Technical Details:

• Data Sourcing: Forex data is typically retrieved from APIs such as OANDA, which provide real-time and historical data.
• Preprocessing: This includes filling missing values using forward fill or interpolation methods, handling outliers through techniques like z-score normalization, and converting timestamps to a uniform format.

2. Feature Engineering

Context

Feature engineering transforms raw data into meaningful features that enhance the model's predictive capabilities. This process is critical for time series analysis as it captures temporal dependencies and seasonality.

Technical Details:

• Lag Features: Introducing past values (lags) as predictors helps capture temporal dependencies.
  • Mathematical Formulation: ( \text{Lag}(k) = X_{t-k} )
• Rolling Statistics: Calculating rolling mean, variance, and standard deviation captures local trends and volatility.
  • Mathematical Formulation: ( \text{Rolling Mean}(w) = \frac{1}{w} \sum_{i=t-w+1}^{t} X_i )
• Scaling: Normalization or standardization ensures that features are on a similar scale, which is essential for models like LSTM and Transformers.

3. Correlation Analysis

Context

Correlation analysis identifies relationships between different forex pairs, which can inform trading strategies and portfolio management.

Technical Details:

• Pearson Correlation: Measures linear correlation between pairs.
  • Formula: ( \rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} )
  • Properties: Symmetric, bounded between -1 and 1.
• Visualization: Heatmaps are used to visualize the correlation matrix, highlighting highly correlated pairs.

4. Trend Identification

Context

Identifying trends helps in understanding the market direction and making informed trading decisions. Techniques like moving averages smooth out short-term fluctuations and highlight longer-term trends.

Technical Details:

• Moving Averages: Simple and exponential moving averages (SMA, EMA) are used.
  • SMA Formula: ( \text{SMA}(n) = \frac{1}{n} \sum_{i=0}^{n-1} X_{t-i} )
  • EMA Formula: ( \text{EMA}(t) = \alpha \cdot X_t + (1-\alpha) \cdot \text{EMA}(t-1) )
• Trend Lines: Connecting significant highs or lows in price data to form resistance and support lines.

5. Model Training

Context

Different machine learning models have different strengths in time series forecasting. This project uses ARIMA, LSTM, and Transformer models.

Technical Details:

ARIMA (AutoRegressive Integrated Moving Average):

• Components: AR (p) - AutoRegression, I (d) - Integration, MA (q) - Moving Average.
  • AR: ( X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + \dots + \phi_p X_{t-p} + \epsilon_t )
  • I: ( Y_t = X_t - X_{t-1} ) (d times differencing)
  • MA: ( X_t = \epsilon_t + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} + \dots + \theta_q \epsilon_{t-q} )
• Use Case: Effective for univariate time series with trends and seasonality.

LSTM (Long Short-Term Memory):

• Architecture: Special type of RNN capable of learning long-term dependencies.
  • Gates: Input, forget, and output gates control the cell state.
  • Equations:
    • Forget Gate: ( f_t = \sigma(W_f \cdot [h_{t-1}, X_t] + b_f) )
    • Input Gate: ( i_t = \sigma(W_i \cdot [h_{t-1}, X_t] + b_i) )
    • Output Gate: ( o_t = \sigma(W_o \cdot [h_{t-1}, X_t] + b_o) )
    • Cell State: ( C_t = f_t * C_{t-1} + i_t * \tilde{C_t} )
• Use Case: Suitable for capturing long-term dependencies in time series data.

Transformers:

• Architecture: Self-attention mechanism allows the model to weigh the importance of different parts of the input sequence.
  • Attention Mechanism: ( \text{Attention}(Q, K, V) = \text{softmax}\left( \frac{QK^T}{\sqrt{d_k}} \right) V )
  • Components: Multi-head attention, feed-forward networks, and positional encodings.
• Use Case: Powerful for sequence modeling tasks, especially when capturing global dependencies.

6. Model Evaluation

Context

Model evaluation is crucial to assess the accuracy and reliability of predictions. RMSE (Root Mean Squared Error) is a standard metric for this purpose.

Technical Details:

• RMSE: Measures the average magnitude of the error.
  • Formula: ( \text{RMSE} = \sqrt{ \frac{1}{n} \sum_{i=1}^n (Y_i - \hat{Y_i})^2 } )
  • Interpretation: Lower RMSE indicates better model performance.

Workflow Summary (Pseudocode)

Data Preparation

1. Ingest data from OANDA.
2. Preprocess data: handle missing values, outliers.
3. Store preprocessed data in TimescaleDB.

Feature Engineering

1. Create lag features and rolling statistics.
2. Store engineered features in TimescaleDB.

Correlation Analysis and Storage

1. Calculate correlation matrix.
2. Store correlation results in TimescaleDB.

Trend Identification and Storage

1. Calculate moving averages and trend indicators.
2. Store trend data in TimescaleDB.

Model Training (ARIMA, LSTM, Transformers)

1. Retrieve feature-engineered data from TimescaleDB.
2. Train ARIMA, LSTM, and Transformer models.
3. Store trained models and scalers.

Model Evaluation and Storage

1. Evaluate models using RMSE.
2. Store evaluation results in TimescaleDB.

Conclusion

This guide provides a detailed, technical overview of the methodologies used in forex time series analysis, leveraging advanced AI/ML models like ARIMA, LSTM, and Transformers. Each step is designed to ensure robustness, scalability, and accuracy in forecasting and trend identification, making it suitable for high-frequency trading environments and financial analytics.