Skip to main content

Part of the book series: The New Palgrave Economics Collection ((NPHE))

Abstract

The importance of Bayesian methods in econometrics has increased rapidly since the early 1990s. This has, no doubt, been fuelled by an increasing appreciation of the advantages that Bayesian inference entails. In particular, it provides us with a formal way to incorporate the prior information we often possess before seeing the data, it fits perfectly with sequential learning and decision making, and it directly leads to exact small sample results. In addition, the Bayesian paradigm is particularly natural for prediction, since we take into account all parameter or even model uncertainty. The predictive distribution is the sampling distribution where the parameters are integrated out with the posterior distribution and provides exactly what we need for forecasting, often a key goal of time-series analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Albert, J. and Chib, S. 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 

  • Barndorff-Nielsen, O. and Shephard, N. 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).

    Article  Google Scholar 

  • Bauwens, L. and Lubrano, M. 1998. Bayesian inference on GARCH models using the Gibbs sampler. Econometrics Journal 1, C23–C46.

    Article  Google Scholar 

  • Bauwens, L., Lubrano, M. and Richard, J.F. 1999. Bayesian Inference in Dynamic Econometric Models. Oxford: Oxford University Press.

    Google Scholar 

  • Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–27.

    Article  Google Scholar 

  • Box, G. and Jenkins, G. 1970. Time Series Analysis: Forecasting and Control. San Francisco: Holden Day.

    Google Scholar 

  • Canova, F. 2004. Testing for convergence clubs in income per capita: a predictive density approach. International Economic Review 45, 49–77.

    Article  Google Scholar 

  • Carter, C. and Kohn, R. 1994. On Gibbs sampling for state space models. Biometrika 81, 541–53.

    Article  Google Scholar 

  • Chib, S. and Greenberg, E. 1994. Bayes inference in regression models with ARMA(p,q) errors. Journal of Econometrics 64, 183–206.

    Article  Google Scholar 

  • de Jong, P. and Shephard, N. 1995. The simulation smoother for time series models. Biometrika 82, 339–50.

    Article  Google Scholar 

  • Durlauf, S. and Johnson, P. 1995. Multiple regimes and cross-country growth behaviour. Journal of Applied Econometrics 10, 365–84.

    Article  Google Scholar 

  • Engle, R. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1008.

    Article  Google Scholar 

  • Escobar, M. and West, M. 1995. Bayesian density-estimation and inference using mixtures. Journal of the American Statistical Association 90, 577–88.

    Article  Google Scholar 

  • Ferguson, T.S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1, 209–230.

    Article  Google Scholar 

  • Fernández, C, Ley, E. and Steel, M. 2001. Model uncertainty in cross-country growth regressions. Journal of Applied Econometrics 16, 563–76.

    Article  Google Scholar 

  • Frühwirth-Schnatter, S. and Kaufmann, S. 2006. Model-based clustering of multiple time series. Journal of Business and Economic Statistics (forthcoming).

    Google Scholar 

  • Gamerman, D. 1997. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Boca Raton, FL: Chapman and Hall/CRC.

    Google Scholar 

  • Garratt, A., Lee, K., Pesaran, H. and Shin, Y. 2003. Forecast uncertainties in macroeconometric modelling: an application to the UK economy. Journal of the American Statistical Association 98, 829–38.

    Article  Google Scholar 

  • Geweke, J. and Terui, N. 1993. Bayesian threshold autoregressive models for nonlinear time series. Journal of Time Series Analysis 14, 441–54.

    Article  Google Scholar 

  • Geweke, J. and Keane, M. 2006. Smoothly mixing regressions. Journal of Econometrics (forthcoming).

    Google Scholar 

  • Granger, C. and Joyeux, R. 1980. An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15–39.

    Article  Google Scholar 

  • Griffin, J. and Steel, M. 2006a. Order-based dependent Dirichlet processes. Journal of the American Statistical Association 101, 179–94.

    Article  Google Scholar 

  • Griffin, J. and Steel, M. 2006b. Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility. Journal of Econometrics 134, 605–44.

    Article  Google Scholar 

  • Hamilton, J. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–84.

    Article  Google Scholar 

  • Harrison, P. and Stevens, C. 1976. Bayesian forecasting. Journal of the Royal Statistical Society Series B 38, 205–17 (with discussion).

    Google Scholar 

  • Harvey, A. 1981. Time Series Models. Oxford: Philip Allen.

    Google Scholar 

  • Harvey, A., Trimbur, T. and van Dijk, H. 2006. Trends and cycles in economic time series: a Bayesian approach. Journal of Econometrics (forthcoming).

    Google Scholar 

  • Hirano, K. 2002. Semiparametric Bayesian inference in autoregressive panel data models. Econometrica 70, 781–99.

    Article  Google Scholar 

  • Hsu, N. and Breidt, F. 2003. Bayesian analysis of fractionally integrated ARMA with additive noise. Journal of Forecasting 22, 491–514.

    Article  Google Scholar 

  • Jacobson, T. and Karlsson, S. 2004. Finding good predictors for inflation: a Bayesian model averaging approach. Journal of Forecasting 23, 479–96.

    Article  Google Scholar 

  • Jacquier, E., Poison, N. and Rossi, P. 1994. Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371–417 (with discussion).

    Google Scholar 

  • Jacquier, E., Poison, N. and Rossi, P. 2004. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122, 185–212.

    Article  Google Scholar 

  • Jensen, M.J. 2004. Semiparametric Bayesian inference of long-memory stochastic volatility models. Journal of Time Series Analysis 25, 895–922.

    Article  Google Scholar 

  • Kleibergen, F. and van Dijk, H. 1993. Non-stationarity in GARCH models: a Bayesian analysis. Journal of Applied Econometrics 8, S41–S61.

    Article  Google Scholar 

  • Koop, G. 2003. Bayesian Econometrics. Chichester: Wiley.

    Google Scholar 

  • Koop, G., Ley, E., Osiewalski, J. and Steel, M. 1997. Bayesian analysis of long memory and persistence using ARFIMA models. Journal of Econometrics 76, 149–69.

    Article  Google Scholar 

  • Koop, G., Osiewalski, J. and Steel, M. 1995. Bayesian long-run prediction in time series models. Journal of Econometrics 69, 61–80.

    Article  Google Scholar 

  • Koop, G. and Potter, S. 1999. Bayes factors and nonlinearity: evidence from economic time series. Journal of Econometrics 88, 251–81.

    Article  Google Scholar 

  • Learner, E. 1978. Specification Searches: Ad Hoc Inference with Nonexperimental Data. New York: Wiley.

    Google Scholar 

  • MacEachern, S. 1994. Estimating Normal means with a conjugate style Dirichlet process prior. Communications in Statistics, B 23, 727–41.

    Article  Google Scholar 

  • Marriott, J., Ravishanker, N., Gelfand, A. and Pai, J. 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 

  • Müller, P. and Quintana, F. 2004. Nonparametric Bayesian data analysis. Statistical Science 19, 95–110.

    Article  Google Scholar 

  • Müller, P., West, M. and MacEachern, S. 1997. Bayesian models for nonlinear autoregressions. Journal of Time Series Analysis 18, 593–614.

    Article  Google Scholar 

  • Odaki, M. 1993. On the invertibility of fractionally differenced ARIMA processes. Biometrika 80, 703–09.

    Article  Google Scholar 

  • Paap, R. and van Dijk, H. 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, 547–63.

    Article  Google Scholar 

  • Pai, J. and Ravishanker, N. 1996. Bayesian modeling of ARFIMA processes by Markov chain Monte Carlo methods. Journal of Forecasting 16, 63–82.

    Article  Google Scholar 

  • Phillips, P. 1991. To criticize the critics: an objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6, 333–473 (with discussion).

    Article  Google Scholar 

  • Roberts, G., Papaspiliopoulos, O. and Dellaportas, P. 2004. Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. Journal of the Royal Statistical Society Series B 66, 369–93.

    Article  Google Scholar 

  • Shephard, N. and Pitt, M. 1997. Likelihood analysis of non-Gaussian measurement time series. Biometrika 84, 653–67.

    Article  Google Scholar 

  • Smith, P.A. and Summers, P.M. 2005. How well do Markov switching models describe actual business cycles? The case of synchronization. Journal of Applied Econometrics 20, 253–74.

    Article  Google Scholar 

  • West, M. and Harrison, P. 1997. Bayesian Forecasting and Dynamic Models, 2nd edn. New York: Springer Verlag.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Copyright information

© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited

About this chapter

Cite this chapter

Steel, M.F.J. (2010). Bayesian time series analysis. In: Durlauf, S.N., Blume, L.E. (eds) Macroeconometrics and Time Series Analysis. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280830_4

Download citation

Publish with us

Policies and ethics