This repository contains the implementation of algorithms outlined in the paper (George Chang & James Feigenbaum (2006) A Bayesian analysis of log-periodic precursors to financial crashes, Quantitative Finance, 6:1, 15-36). Since the paper was published in 2006, the algorithms it proposes have not been available in a coded form. In response, I developed code to replicate the paper’s results. My methodology relied on the Markov Chain Monte Carlo (MCMC) method, specifically utilizing the Metropolis-Hastings Algorithm within Gibbs Sampler (referred to as Metropolis within Gibbs), to accurately reproduce the findings of the original study.
- data: the S&P 500 index data spanning from 01/02/1980 to 12/30/1988 (
S&P_500_Index_01021980_12301988_preprocessed.csv)
(For comprehensive details and structures about Metropolis within Gibbs employed in this code, please refer to Implementation of “A Bayesian analysis of log-periodic precursors to financial crashes” paper in R)
- Execute
utils_BLPPL_posterior.R. - Select a combination of prior distributions and time models.
- prior distributions: diffuse priors, tight priors
- time models: calendar time model, market time model
- Navigate to the folder corresponding to your chosen combination.
ex. For diffuse priors & calendar time model, go to BLPPL_sampling_posterior(diffuse_priors_calendar_time). - Execute
BLPPL_posterior(chosen combination).Rto obtain posterior samples for each parameter.
ex. For diffuse priors & calendar time model, run BLPPL_posterior(Diffuse_priors_Calendar_time).R. - To analyze the posterior distribution, execute
checking_results(chosen combination).R.
ex. For diffuse priors & calendar time model, run checking_results(Diffuse_priors_Calendar_time).R. - A posterior sample of parameters at each iteration allows for plotting a line using the LPPL Model equation. To address uncertainty, the Bayesian approach advocates using a credible interval. I have thus developed a code (
posterior_credible_interval.R) that plots a 95% credible interval alongside the actual S&P 500 index data. This feature represents a novel contribution of my code, as the original paper did not discuss the use of a 95% credible interval.
For any inquiries, you can reach me at sjung055@yonsei.ac.kr.