8.5 Summary

We present a brief review of Bayesian inference in time series models. In particular, we introduce the state-space representation and demonstrate how to perform inferential analysis for these models, focusing on the dynamic linear model and the stochastic volatility model. Additionally, we show how ARMA(p,q) processes can be expressed in state-space form and provide methods for estimating such models.

We also include code for implementing computational inference algorithms, such as sequential Monte Carlo (SMC), Hamiltonian Monte Carlo (HMC), and various Markov chain Monte Carlo (MCMC) methods. Finally, we introduce VAR(p) models, detailing how to perform impulse-response analysis and forecasting within this framework.

Time series analysis is a highly active research area with remarkable methodological developments and applications. Interested readers can refer to excellent materials in chapters 7 and 9 of John Geweke, Koop, and Dijk (2011), and chapters 17 to 20 of Chan et al. (2019), along with the references therein.

References

Chan, Joshua, Gary Koop, Dale J Poirier, and Justin L Tobias. 2019. Bayesian Econometric Methods. Vol. 7. Cambridge University Press.

Geweke, John, Gary Koop, and Herman K van Dijk. 2011. The Oxford Handbook of Bayesian Econometrics. Oxford University Press, USA.