Principal Component Analysis and Hidden Markov Model for Forecasting Stock Returns

ArXiv ID: 2307.00459 “View on arXiv”

Authors: Unknown

Abstract

This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to the covariance matrix of stock returns for companies listed in the S&P 500 index, and interpreting principal components as factor returns, we apply the HMM model on them. Then we use the transition probability matrix and state conditional means to forecast the factors returns. Reverting the factor returns forecasts to stock returns using eigenvectors, we obtain forecasts for the stock returns. We find that, with the right hyperparameters, our model yields a strategy that outperforms the buy-and-hold strategy in terms of the annualized Sharpe ratio.

Keywords: Principal component analysis (PCA), Hidden Markov model (HMM), S&P 500 index, Stock return forecasting, Equities (Stocks)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like spectral theorem for symmetric matrices, eigen-decomposition, and Gaussian HMMs, resulting in high math complexity. It also demonstrates strong empirical rigor by applying the method to S&P 500 data, implementing trading strategies, and reporting performance metrics like annualized Sharpe ratio against a benchmark.

  flowchart TD
    Goal["Research Goal: Forecast Stock Returns & Outperform Buy-and-Hold"] -->|Input| Data["Data: S&P 500 Historical Returns"]
    Data -->|Process 1| PCA["PCA: Decompose Covariance Matrix into Principal Components (Factors)"]
    PCA -->|Output| Factors["Factor Returns (Eigenvectors)"]
    Factors -->|Process 2| HMM["HMM: Model Factor Dynamics & Forecast Returns"]
    HMM -->|Output| Forecast["Forecasted Stock Returns"]
    Forecast -->|Process 3| Strategy["Trading Strategy: Reconstruct & Trade"]
    Strategy -->|Result| Outcome["Outcome: Annualized Sharpe Ratio > Buy-and-Hold"]