1. Home
  2. Volume 6 - Number 2
  3. Forecasting with Bayesian vector autoregressive models: comparison of direct and iterated multistep methods
New submission
Issues
Journal Information
Aims and ScopeEditorial BoardEditorial Advisory BoardJournal Policies
Resources
For Readers
For Authors
For Editors
For Reviewers
Publication EthicsCall for Special Issue
ISSN
ISSN 2615-9821
ISSN(Previous) 2588-1396

Volume 6 - Number 2 | July 2022

Forecasting with Bayesian vector autoregressive models: comparison of direct and iterated multistep methods

Katsuhiro Sugita

20/07/2022 144 0 0
Like Buy now 20.000 đ
Forecasting Bayesian econometrics VAR model

Abstract:

Purpose
The paper compares multi-period forecasting performances by direct and iterated method using Bayesian vector autoregressive (VAR) models.

Design/methodology/approach
The paper adopts Bayesian VAR models with three different priors – independent Normal-Wishart prior, the Minnesota prior and the stochastic search variable selection (SSVS). Monte Carlo simulations are conducted to compare forecasting performances. An empirical study using US macroeconomic data are shown as an illustration.

Findings
In theory direct forecasts are more efficient asymptotically and more robust to model misspecification than iterated forecasts, and iterated forecasts tend to bias but more efficient if the one-period ahead model is correctly specified. From the results of the Monte Carlo simulations, iterated forecasts tend to outperform direct forecasts, particularly with longer lag model and with longer forecast horizons. Implementing SSVS prior generally improves forecasting performance over unrestricted VAR model for either nonstationary or stationary data.

Originality/value
The paper finds that iterated forecasts using model with the SSVS prior generally best outperform, suggesting that the SSVS restrictions on insignificant parameters alleviates over-parameterized problem of VAR in one-step ahead forecast and thus offers an appreciable improvement in forecast performance of iterated forecasts.

References:

  1. Ang, A., Piazzesi, M. and Wei, M. (2006), “What does the yield curve tell us about GDP growth?”, Journal of Econometrics, Vol. 131 Nos 1-2, pp. 359-403.
  2. Bhansali, R.J. (1996), “Asymptotically efficient autoregressive model selection for multistep prediction”, Annals of the Institute of Statistical Mathematics, Vol. 48 No. 3, pp. 577-602.
  3. Bhansali, R. (1997), “Direct autoregressive predictors for multistep prediction: order selection and performance relative to the plug in predictors”, Statistica Sinica, Vol. 7, pp. 425-449.
  4. Chevillon, G. and Hendry, D.F. (2005), “Non-parametric direct multi-step estimation for forecasting economic processes”, International Journal of Forecasting, Vol. 21 No. 2, pp. 201-218.
  5. Clements, M.P. and Hendry, D.F. (1996), “Multi-step estimation for forecasting”, Oxford Bulletin of Economics and Statistics, Vol. 58 No. 4, pp. 657-684.
  6. Cogley, T. and Sargent, T.J. (2005), “Drifts and volatilities: monetary policies and outcomes in the post WWII US”, Review of Economic Dynamics, Vol. 8 No. 2, pp. 262-302.
  7. Doornik, J.A. (2013), Object-Oriented Matrix Programming Using Ox, Timberlake Consultants Press, London.
  8. George, E.I. and McCulloch, R.E. (1997), “Approaches for Bayesian variable selection”, Statistica Sinica, Vol. 7, pp. 339-373.
  9. George, E.I., Sun, D. and Ni, S. (2008), “Bayesian stochastic search for VAR model restrictions”, Journal of Econometrics, Vol. 142 No. 1, pp. 553-580.
  10. Ing, C.-k. (2003), “Multistep prediction in autoregressive processes”, Econometric Theory, Vol. 19 No. 2, pp. 254-279.
  11. Jochmann, M., Koop, G. and Strachan, R.W. (2010), “Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks”, International Journal of Forecasting, Vol. 26 No. 2, pp. 326-347, doi: 10.1016/j.ijforecast.2009.11.002.
  12. Jochmann, M., Koop, G., León-González, R. and Strachan, R.W. (2013), “Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy”, Journal of Applied Econometrics, Vol. 28 No. 4, pp. 62-81.
  13. Kang, I.B. (2003), “Multi-period forecasting using different models for different horizons: an application to US economic time series data”, International Journal of Forecasting, Vol. 19 No. 3, pp. 387-400.
  14. Koop, G., Leon-Gonzalez, R. and Strachan, R.W. (2009), “On the evolution of the monetary policy transmission mechanism”, Journal of Economic Dynamics and Control, Vol. 33 No. 4, pp. 997-1017.
  15. Litterman, R.B. (1986), “Forecasting with Bayesian vector autoregressions: five year experience”, Journal of Business Economic Statistics, Vol. 4 No. 1, pp. 25-38.
  16. Marcellino, M., Stock, J.H. and Watson, M.W. (2006), “A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series”, Journal of Econometrics, Vol. 135 No. 1, pp. 499-526.
  17. Pesaran, M.H., Pick, A. and Timmermann, A. (2011), “Variable selection, estimation and inference for multi-period forecasting problems”, Journal of Econometrics, Vol. 164 No. 1, pp. 173-187.
  18. Primiceri, G.E. (2005), “Time varying structural vector autoregressions and monetary policy”, Review of Economic Studies, Vol. 72 No. 3, pp. 821-852.
  19. Sugita, K. (2018), Evaluation of forecasting performance using Bayesian stochastic search variable selection in a vector autoregression, Ryukyu Economics Working Paper #1, University of the Ryukyus.
  20. Sugita, K. (2019a), Forecasting with vector autoregressions by Bayesian model averaging, Ryukyu Economics Working Paper #3, University of the Ryukyus.
  21. Sugita, K. (2019b), Forecasting with vector autoregressions using Bayesian variable selection methods: comparison of direct and iterated methods, Ryukyu Economics Working Paper #2, University of the Ryukyus.

 

Related articles