The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Bayesian Time Series Analysis

  • Mark F. J. Steel
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2737

Abstract

This article describes the use of Bayesian methods in the statistical analysis of time series. The use of Markov chain Monte Carlo methods has made even the more complex time series models amenable to Bayesian analysis. Models discussed in some detail are ARIMA models and their fractionally integrated counterparts, state space models, Markov switching and mixture models, and models allowing for time-varying volatility. A final section reviews some recent approaches to nonparametric Bayesian modelling of time series.

Keywords

ARCH models ARFIMA models ARIMA models ARMA models Bayes factor Bayesian inference Bayesian methods in econometrics Bayesian model averaging Bayesian nonparametrics Bayesian time series analysis Business cycles Cointegration Computational algorithms Conditional likelihood Continuous-time models Convergence clubs Data augmentation Dirichlet processes Forecasting GARCH models Gibbs sampler Growth regressions Hidden Markov models Impulse response function Kalman filter latent states Lévy processes Long-memory models Macroeconomic forecasting Markov chain Monte Carlo methods Markov switching models Metropolis Hastings sampler Nonparametric models Ornstein–Uhlenbeck processes Posterior odds Prediction Prior odds Regime switching models Regression Sequential learning Spatial statistics State space models Stochastic volatility models Survival analysis Threshold autoregressive models Time series analysis Uncertainty Unit roots Vector autoregressions 
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Bibliography

  1. Albert, J., and S. Chib. 1993. Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. Journal of Business and Economic Statistics 11: 1–15.Google Scholar
  2. Barndorff-Nielsen, O., and N. Shephard. 2001. Non-Gaussian OU based models and some of their uses in financial economics. Journal of the Royal Statistical Society Series B 63: 167–241 (with discussion).CrossRefGoogle Scholar
  3. Bauwens, L., and M. Lubrano. 1998. Bayesian inference on GARCH models using the Gibbs sampler. Econometrics Journal 1: C23–C46.CrossRefGoogle Scholar
  4. Bauwens, L., M. Lubrano, and J.F. Richard. 1999. Bayesian inference in dynamic econometric models. Oxford: Oxford University Press.Google Scholar
  5. Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31: 307–327.CrossRefGoogle Scholar
  6. Box, G., and G. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden Day.Google Scholar
  7. Canova, F. 2004. Testing for convergence clubs in income per capita: A predictive density approach. International Economic Review 45: 49–77.CrossRefGoogle Scholar
  8. Carter, C., and R. Kohn. 1994. On Gibbs sampling for state space models. Biometrika 81: 541–553.CrossRefGoogle Scholar
  9. Chib, S., and E. Greenberg. 1994. Bayes inference in regression models with ARMA (p, q) errors. Journal of Econometrics 64: 183–206.CrossRefGoogle Scholar
  10. de Jong, P., and N. Shephard. 1995. The simulation smoother for time series models. Biometrika 82: 339–350.CrossRefGoogle Scholar
  11. Durlauf, S., and P. Johnson. 1995. Multiple regimes and cross-country growth behaviour. Journal of Applied Econometrics 10: 365–384.CrossRefGoogle Scholar
  12. Engle, R. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987–1008.CrossRefGoogle Scholar
  13. Escobar, M., and M. West. 1995. Bayesian density-estimation and inference using mixtures. Journal of the American Statistical Association 90: 577–588.CrossRefGoogle Scholar
  14. Ferguson, T.S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1: 209–230.CrossRefGoogle Scholar
  15. Fernández, C., E. Ley, and M. Steel. 2001. Model uncertainty in cross-country growth regressions. Journal of Applied Econometrics 16: 563–576.CrossRefGoogle Scholar
  16. Frühwirth-Schnatter, S., and S. Kaufmann. 2006. Model-based clustering of multiple time series. Journal of Business and Economic Statistics 26: 78–89.CrossRefGoogle Scholar
  17. Gamerman, D. 1997. Markov chain Monte Carlo: Stochastic simulation for Bayesian inference. Boca Raton: Chapman and Hall/CRC.Google Scholar
  18. Garratt, A., K. Lee, H. Pesaran, and Y. Shin. 2003. Forecast uncertainties in macroeconometric modelling: An application to the UK economy. Journal of the American Statistical Association 98: 829–838.CrossRefGoogle Scholar
  19. Geweke, J., and M. Keane. 2006. Smoothly mixing regressions. Journal of Econometrics 138: 291–311.Google Scholar
  20. Geweke, J., and N. Terui. 1993. Bayesian threshold autoregressive models for nonlinear time series. Journal of Time Series Analysis 14: 441–454.CrossRefGoogle Scholar
  21. Granger, C., and R. Joyeux. 1980. An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1: 15–39.CrossRefGoogle Scholar
  22. Griffin, J., and M. Steel. 2006a. Order-based dependent Dirichlet processes. Journal of the American Statistical Association 101: 179–194.CrossRefGoogle Scholar
  23. Griffin, J., and M. Steel. 2006b. Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility. Journal of Econometrics 134: 605–644.CrossRefGoogle Scholar
  24. Hamilton, J. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357–384.CrossRefGoogle Scholar
  25. Harrison, P., and C. Stevens. 1976. Bayesian forecasting. Journal of the Royal Statistical Society Series B 38: 205–247 (with discussion).Google Scholar
  26. Harvey, A. 1981. Time series models. Oxford: Philip Allen.Google Scholar
  27. Harvey, A., T. Trimbur, and H. van Dijk. 2006. Trends and cycles in economic time series: A Bayesian approach. Journal of Econometrics 140: 618–649.CrossRefGoogle Scholar
  28. Hirano, K. 2002. Semiparametric Bayesian inference in autoregressive panel data models. Econometrica 70: 781–799.CrossRefGoogle Scholar
  29. Hsu, N., and F. Breidt. 2003. Bayesian analysis of fractionally integrated ARMA with additive noise. Journal of Forecasting 22: 491–514.CrossRefGoogle Scholar
  30. Jacobson, T., and S. Karlsson. 2004. Finding good predictors for inflation: A Bayesian model averaging approach. Journal of Forecasting 23: 479–496.CrossRefGoogle Scholar
  31. Jacquier, E., N. Polson, and P. Rossi. 1994. Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12: 371–417 (with discussion).Google Scholar
  32. Jacquier, E., N. Polson, and P. Rossi. 2004. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122: 185–212.CrossRefGoogle Scholar
  33. Jensen, M.J. 2004. Semiparametric Bayesian inference of long-memory stochastic volatility models. Journal of Time Series Analysis 25: 895–922.CrossRefGoogle Scholar
  34. Kleibergen, F., and H. van Dijk. 1993. Non-stationarity in GARCH models: A Bayesian analysis. Journal of Applied Econometrics 8: S41–S61.CrossRefGoogle Scholar
  35. Koop, G. 2003. Bayesian econometrics. Chichester: Wiley.Google Scholar
  36. Koop, G., and S. Potter. 1999. Bayes factors and nonlinearity: Evidence from economic time series. Journal of Econometrics 88: 251–281.CrossRefGoogle Scholar
  37. Koop, G., J. Osiewalski, and M. Steel. 1995. Bayesian long-run prediction in time series models. Journal of Econometrics 69: 61–80.CrossRefGoogle Scholar
  38. Koop, G., E. Ley, J. Osiewalski, and M. Steel. 1997. Bayesian analysis of long memory and persistence using ARFIMA models. Journal of Econometrics 76: 149–169.CrossRefGoogle Scholar
  39. Leamer, E. 1978. Specification searches: Ad Hoc inference with nonexperimental data. New York: Wiley.Google Scholar
  40. MacEachern, S. 1994. Estimating normal means with a conjugate style dirichlet process prior. Communications in Statistics B 23: 727–741.CrossRefGoogle Scholar
  41. Marriott, J., N. Ravishanker, A. Gelfand, and J. Pai. 1996. Bayesian analysis of ARMA processes: Complete sampling-based inference under exact likelihoods. In Bayesian analysis in statistics and econometrics, ed. D. Berry, K. Chaloner, and J. Geweke. New York: Wiley.Google Scholar
  42. Müller, P., and F. Quintana. 2004. Nonparametric Bayesian data analysis. Statistical Science 19: 95–110.CrossRefGoogle Scholar
  43. Müller, P., M. West, and S. MacEachern. 1997. Bayesian models for nonlinear autoregressions. Journal of Time Series Analysis 18: 593–614.CrossRefGoogle Scholar
  44. Odaki, M. 1993. On the invertibility of fractionally differenced ARIMA processes. Biometrika 80: 703–709.CrossRefGoogle Scholar
  45. Paap, R., and H. van Dijk. 2003. Bayes estimation of Markov trends in possibly cointegrated series: An application to U.S. consumption and income. Journal of Business and Economic Statistics 21: 547–563.CrossRefGoogle Scholar
  46. Pai, J., and N. Ravishanker. 1996. Bayesian modeling of ARFIMA processes by Markov chain Monte Carlo methods. Journal of Forecasting 16: 63–82.CrossRefGoogle Scholar
  47. Phillips, P. 1991. To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6: 333–473 (with discussion).CrossRefGoogle Scholar
  48. Roberts, G., O. Papaspiliopoulos, and P. Dellaportas. 2004. Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. Journal of the Royal Statistical Society, Series B 66: 369–393.CrossRefGoogle Scholar
  49. Shephard, N., and M. Pitt. 1997. Likelihood analysis of non-Gaussian measurement time series. Biometrika 84: 653–667.CrossRefGoogle Scholar
  50. Smith, P.A., and P.M. Summers. 2005. How well do Markov switching models describe actual business cycles? The case of synchronization. Journal of Applied Econometrics 20: 253–274.CrossRefGoogle Scholar
  51. West, M., and P. Harrison. 1997. Bayesian forecasting and dynamic models, 2nd ed. New York: Springer.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Mark F. J. Steel
    • 1
  1. 1.