Modeling the Stock Market Using the Ising Model

This notebook models the stock market using the Ising model, inspired by the paper "The stock market learned as Ising model" by L. Zhao, W. Bao, and W. Li.

Overview

We analyze financial data from three major stock indices:

• S&P 500 (US)
• FTSE 250 (UK)
• SSE 380 (China)

The notebook performs the following key steps:

1. Data Acquisition:

   • Fetch stock tickers for each index.
   • Download adjusted closing prices from Yahoo Finance using yfinance.
   • For SSE 380, scrape tickers from the Shanghai Stock Exchange website using Selenium.

2. Data Preprocessing:

   • Compute logarithmic returns of stock prices.
   • Binarize returns into spin states (( s_i = \pm 1 )) to represent positive or negative returns.
   • Filter out stocks with insufficient data points.
   • Align datasets by common dates and truncate to equal lengths.

3. Correlation Analysis:

   • Compute and visualize the correlation matrix of stock returns.
   • Analyze the mean, median, and mode of off-diagonal correlation coefficients.

4. Ising Model Implementation:

   • Naive Mean Field (nMF) Approximation:
     • Compute mean magnetizations and covariance matrix.
     • Estimate coupling strengths ( J_{ij}^{\text{nMF}} ) and external fields ( h_i^{\text{nMF}} ).
   • Thouless-Anderson-Palmer (TAP) Approximation:
     • Include higher-order corrections for coupling strengths ( J_{ij}^{\text{TAP}} ) and external fields ( h_i^{\text{TAP}} ).

5. Statistical Analysis:

   • Calculate statistical moments (mean, variance, skewness, kurtosis) of coupling strengths.
   • Filter out extreme coupling values by removing the top and bottom 5% to reduce the impact of outliers.
   • Shuffle data to remove correlations and recompute coupling strengths for significance testing.

6. Visualization:

   • Plot histograms of coupling strength distributions for both original and shuffled data.
   • Visualize external field distributions to understand individual stock tendencies.
   • Generate heatmaps of the coupling matrices to identify interaction patterns between stocks.

How to Use This Notebook

1. Install Required Packages:

   !pip install yfinance seaborn

2. Import Libraries:

   • Ensure all necessary libraries are imported, including numpy, pandas, yfinance, seaborn, matplotlib, and scipy.

3. Data Acquisition:

   • Run the provided functions to fetch and load stock data for S&P 500, FTSE 250, and SSE 380.
   • Save the datasets to CSV files for future use.

4. Data Preprocessing:

   • Compute logarithmic returns and binarize them into spin states.
   • Filter stocks with sufficient data and align datasets across all markets.

5. Correlation Analysis:

   • Compute the correlation matrix and visualize it using a heatmap.

6. Ising Model Computation:

   • Use the provided functions to compute coupling strengths and external fields using both nMF and TAP approximations.
   • Apply regularization to covariance matrices to ensure numerical stability.

7. Statistical Analysis and Filtering:

   • Filter out extreme coupling strengths by removing the top and bottom 5% of values.
   • Shuffle the data and repeat the analysis for comparison.

8. Visualization:

   • Plot coupling strength distributions and external field distributions.
   • Visualize coupling matrices using heatmaps with stock tickers as axis labels.

9. Interpretation:

   • Analyze the results to understand the interactions and tendencies within each stock market.
   • Compare the original and shuffled data to assess the significance of the inferred interactions.

Dependencies

• Python 3.x
• Packages:
  • numpy
  • pandas
  • yfinance
  • seaborn
  • matplotlib
  • scipy
  • selenium (for web scraping SSE 380 tickers)
  • webdriver-manager (optional, for Selenium)

Notes

• Data Fetching: Fetching data from Yahoo Finance and scraping websites may take time and requires an active internet connection.
• Selenium Setup: Scraping SSE 380 tickers with Selenium may require additional setup, such as installing ChromeDriver.
• Data Files: Datasets are saved as CSV files for convenience.
• Execution Order: Run the notebook cells sequentially to avoid errors.
• Visualization: Adjustments may be needed for visualization parameters based on the data and display preferences.