Markov Switching Model for Financial Time Series

This project implements a Bayesian Markov Switching Model for analyzing financial time series data, with a particular focus on capturing the peculiar dynamics of stock returns. The model employs a full Bayesian approach to identify and characterize different market regimes, providing a robust framework for understanding market behavior.

Project Overview

Financial time series analysis presents several modeling challenges:

1. Regime-Switching Behavior: Markets transition between distinct states (e.g., bull markets, bear markets)
2. Volatility Dynamics: Returns generally show persistent volatility patterns and clustering
3. Non-Normal Features: Returns often display fat tails and excess kurtosis
4. Mean Reversion: Returns exhibit varying degrees of mean reversion across regimes

The project addresses these challenges through a Markov Switching Model that:

• Uses latent state variables to identify market regimes
• Implements regime-specific dynamics for returns and volatility
• Incorporates prior knowledge (or lack of) via Bayesian priors
• Provides full posterior distributions for all model parameters (thanks to the Bayesian approach)

Analysis and Implementation

1. Exploratory Data Analysis

The EDA component provides a detailed statistical analysis for understanding financial time series behavior:

• Statistical Tests: Tests including Jarque-Bera, Augmented Dickey-Fuller, and Ljung-Box
• Distribution Analysis: Examination of return distributions and normality
• Volatility Analysis: Investigation of volatility clustering, persistence, and leverage effects
• Time Series Properties: Analysis of autocorrelation patterns in returns and squared returns

2. Bayesian Markov Switching Model

Building on the insights from the EDA, the Markov Switching Model is implemented via a Bayesian approach:

• Hidden Markov Chain: Latent state variables following a Markov process
• Regime-Specific Parameters:
  • Mean returns with autoregressive components
  • Volatility dynamics with GARCH-like features
  • Transition probabilities between regimes
• Prior Specifications:
  • Beta priors for transition probabilities
  • Normal priors for mean returns
  • Half-Normal priors for volatility parameters
  • Stationarity constraints for autoregressive components

3. Volatility Modeling

The model implements a volatility modeling approach that:

• Combines base volatility levels with regime-specific dynamics
• Incorporates ARCH-like components responding to recent returns
• Includes a memory component with adaptive weighting
• Ensures stationarity through parameter constraints

4. Inference and Analysis

The project provides tools for:

• MCMC sampling with NUTS algorithm
• Posterior predictive analysis
• Regime probability estimation
• Model diagnostics and convergence checks
• Visualization of regime classifications and parameter distributions

Project Structure

• EDA_analysis.ipynb: Comprehensive statistical analysis of financial time series
• MSModel_2Regimes.ipynb: Core implementation of the Markov Switching Model
• stock.py: Stock data handling and preprocessing
• aux.py: Utility functions for analysis and visualization

Installation

1. Clone this repository:

git clone https://github.com/yourusername/markov_switching.git
cd markov_switching

2. Install the required dependencies:

pip install -r requirements.txt