Bayesian Nonlinear Ornstein-Uhlenbeck Models with Stochastic Volatility.

bayesianOU

Bayesian Nonlinear Ornstein-Uhlenbeck Models with Stochastic Volatility

Overview

The bayesianOU package fits Bayesian nonlinear Ornstein-Uhlenbeck models with cubic drift, stochastic volatility (SV), and Student-t innovations. It implements hierarchical priors for sector-specific parameters and supports parallel MCMC sampling via Stan.

Installation

# Install from GitHub (development version)
# install.packages("remotes")
remotes::install_github("author/bayesianOU")

# For Stan backend, you need either cmdstanr or rstan
# cmdstanr (recommended):
install.packages("cmdstanr", repos = c("https://mc-stan.org/r-packages/", getOption("repos")))
cmdstanr::install_cmdstan()

# Or rstan:
install.packages("rstan")

Quick Start

library(bayesianOU)

# Prepare data
Y <- as.matrix(your_prices_data)
X <- as.matrix(your_production_prices_data)
TMG <- your_tmg_series
COM <- as.matrix(your_com_data)
K <- as.matrix(your_capital_data)

# Fit model
results <- fit_ou_nonlinear_tmg(
  results_robust = list(),
  Y = Y, X = X, TMG = TMG, COM = COM, CAPITAL_TOTAL = K,
  chains = 4, iter = 8000, warmup = 4000,
  verbose = TRUE
)

# Validate fit
validate_ou_fit(results)

# Extract convergence evidence
conv <- extract_convergence_evidence(results)

# Plot results
plot_beta_tmg(results)
plot_drift_curves(results)

Model Specification

The model implements a nonlinear OU process with cubic drift:

$$dY_t = \kappa(\theta - Y_t + a_3 (Y_t - \theta)^3) dt + \sigma_t dW_t$$

where:

• $\kappa_s$ is the sector-specific mean reversion speed
• $\theta_s$ is the sector-specific equilibrium level
• $a_3$ is the cubic nonlinearity coefficient
• $\sigma_t$ follows an AR(1) stochastic volatility process
• Innovations are Student-t distributed with estimated degrees of freedom

Features

• Hierarchical priors for sector-specific parameters
• Stochastic volatility with AR(1) log-variance
• Student-t innovations for fat tails
• Parallel likelihood computation via Stan's reduce_sum
• PSIS-LOO cross-validation for model comparison
• Out-of-sample forecast evaluation

Citation

If you use this package, please cite:

@software{bayesianOU,
  author = {Author Name},
  title = {bayesianOU: Bayesian Nonlinear Ornstein-Uhlenbeck Models},
  year = {2024},
  url = {https://github.com/author/bayesianOU}
}

References

• Stan User's Guide (SV, HMM, parallelization)
• Vehtari, Gelman, Gabry (2017). Practical Bayesian model evaluation using leave-one-out cross-validation. Statistics and Computing.
• Gelman (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis.

License

MIT License.