Bayesian Nonparametric Change-Point Detection for Macroeconomic Time Series

Project Description

This project implements a custom Bayesian Nonparametric (BNP) model to perform change-point detection and regime clustering on U.S. macroeconomic time series. The algorithm utilizes Reversible-Jump Markov Chain Monte Carlo (MCMC) methods with Parallel Tempering to explore the parameter space and identify structural breaks in the economy, such as the impact of the COVID-19 pandemic.

Dataset

The analysis is based on a combined dataset of three key macroeconomic indicators (monthly frequency, starting from August 1982):

• UNRATE: Civilian Unemployment Rate.
• CPIAUCSL: Consumer Price Index for All Urban Consumers.
• REAINTRATREARAT10Y: 10-Year Real Interest Rate.

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Methodology

1. Algorithm & MCMC Configuration

• Parallel Tempering: Implemented using 4 different temperature chains (T = {1, 2, 4, 8}) to improve the exploration of the posterior distribution and avoid local optima.
• Partition Updates: The algorithm proposes changes to the time series partitions using custom Split, Merge, and Shuffle moves.
• Parameter Inference: Metropolis-Hastings steps are used to update the hyperparameters (gamma, sigma, theta) governing the regime distributions.

2. Convergence & Diagnostics

• The coda package is used to evaluate MCMC convergence.
• Diagnostics included: Trace plots, Density plots, Autocorrelation plots (ACF), and Gelman-Rubin diagnostics across the multiple chains.

3. Optimal Partition Selection

• To summarize the MCMC output, the project constructs a Posterior Similarity Matrix (PSM).
• The final optimal partition (regime identification) is selected by minimizing the Variation of Information (VI) loss function using tools from the BNPmix package.

4. Results & Visualization

• Credible Intervals: Calculated for parameters (gamma, sigma, theta) within each identified regime.
• Posterior Probabilities: Plotted to show the probability of regime membership over time.
• Time Series Annotation: The raw time series are plotted with vertical dashed lines representing the identified change-points (e.g., automatically flagging the 2020-03-01 COVID-19 shock).

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Requirements and Libraries

The project heavily relies on a mix of R and C++ code (Rcpp, RcppArmadillo) for performance optimization. Key R packages used include: BNPmix, coda, ggplot2, dplyr, tidyr, LaplacesDemon, mvtnorm, and patchwork. Custom C++ functions (cpp_funz.cpp, wade.cpp) and R scripts for log-likelihood and alpha calculations are sourced directly in the main pipeline.