Bayesian Change-point Model for ARCH

Nam, Seung-Min;Kim, Ju-Won;Cho, Sin-Sup

  • 발행 : 2006.12.31


We consider a multiple change point model with autoregressive conditional heteroscedasticity (ARCH). The model assumes that all or the part of the parameters in the ARCH equation change over time. The occurrence of the change points is modelled as the discrete time Markov process with unknown transition probabilities. The model is estimated by Markov chain Monte Carlo methods based on the approach of Chib (1998). Simulation is performed using a variant of perfect sampling algorithm to achieve the accuracy and efficiency. We apply the proposed model to the simulated data for verifying the usefulness of the model.


Bayesian change-point;Markov chain;perfect sampler


  1. Berkes, I, Gornbay, E., Horvath, L., Kokoszka, P. (2004). Sequential change-point detection in GARCH(p,q) models. Econometric Theory, Vol. 20, 1140-1167
  2. Bollerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, Vol. 31, 307-327
  3. Cassella, G., Lavine, M. and Robert, C. (2000), Explaining the perfect sampler. Working paper 00-16, State University of New York at Stony Brook, Duke University, Durham
  4. Chib, S. (1996), Calculating posterior distributions and modal estimates in Markov mixture models. Journal of Econometrics, Vol. 75, 79-98
  5. Chib, S. (1998), Estimation and Comparison of Multiple Change-point Models. Journal of Econometrics, Vol. 86, 221-241
  6. Corcoran, J. and Tweedie, R. (2002), Perfect sampling from Independent Metropolis-Hastings Chains. Journal of Statistical Planning and Inference, Vol. 104, 297-314
  7. Corcoran, J. and Schneider, U. (2005), Pseudo-perfect and adaptive variants of the Metropolis-Hastings algorithm with an independent candidate density. Journal of Statistical Computation and Simulation, Vol. 75, 459-475
  8. Geweke, J. (1989), Exact predictive densities in linear models with ARCH disturbances. Journal of Econometrics, Vol. 40, 63-86
  9. Geweke, J. (1994), Bayesian comparison of econemetric models. Working Paper 532, Research Department, Federal Reserve Bank of Minneapolis
  10. Kaufmann, S. and FrUhwirth-Schanatter, S. (2002), Bayesian Analysis of Switching ARCH models. Journal of Time Series Analysis, Vol. 23, 425-458
  11. Kim, S., Shephard, N. and Chib, S. (1998), Stochastic volatility : Likelihood inference and comparison with ARCH models. Review of Economics Studies, Vol. 65, 361-393
  12. Kokoszka, P. and Leipus, R. (2000), Change-point estimation in ARCH models. Bernoulli, Vol. 6, 513-539
  13. Nakatsuma, T. (2000), Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach. Journal of Econometrics, Vol. 95, 57-69
  14. Nelson, D. (1991), Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, Vol. 59, 347-370
  15. Engle, R. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, Vol. 50, 987-1008
  16. Propp, J. and Wilson, D. (1996), Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures and Algorithms, Vol. 9, 223-252<223::AID-RSA14>3.0.CO;2-O