- Published by:
- Department of Treasury and Finance
- Date:
- 1 Nov 2023
Hamish McLean, Jonathan Dark1
1. Department of Finance, University of Melbourne and The Department of Treasury and Finance.
Author contact details: veb@dtf.vic.gov.au.
Disclaimer: The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Victorian Department of Treasury and Finance (DTF).
Suggested Citation: Hamish McLean and Jonathan Dark (2023), Prediction intervals for model combinations of direct and iterated forecasts with an application to forecasting Australian household consumption. Victoria’s Economic Bulletin, November 2023, vol 7, no 2. DTF.
Abstract
The increasing availability of high frequency data and the desire for timely forecast updates, has seen widespread use of the Mixed data sampling (MIDAS) model. This model for example can generate forecasts of a monthly or quarterly variable using a daily predictor. If required, this means forecasts can be updated each day.
MIDAS models employ direct forecasts as opposed to more traditional models (like ARMA or VAR) that generate forecasts iteratively. Point forecasts from model combinations of direct and iterated forecasts are common, however there has been no attempt to construct intervals around these predictions. In this paper, we propose a new bootstrapping technique for prediction interval (PI) estimation around combinations of iterated and direct forecasts.
We applied the procedure to out‑of‑sample forecasts of Australian household consumption and find that our procedure generates PIs consistent with the level of confidence during normal periods. However, during crises periods, our predictions appear less reliable given the high rates of PI violation observed. Our results support the use of MIDAS models fit to high‑frequency regressors to address this problem. On predicting household consumption, we found that direct measures of spending activity (such as credit card payment) and underemployment provide the most information. And despite being more forward looking, financial market data was not very useful.
1. Introduction
The speed of transitions in modern economies and the availability of high‑frequency data has increased the need for timely forecasts that utilise all available information.
2. The MIDAS class of models
Traditional econometric frameworks require all data to be measured at the same frequency.
3. Bootstrapped prediction interval estimation
We develop our approach by initially reviewing the standard bootstrap approach to prediction interval estimation in section 3.1.
4. Empirical application
In this section we forecast Australian household consumption from Q3 2003 to Q2 2022 via rolling windows.
5. Conclusion
We proposed a bootstrapping technique for prediction interval estimation around combinations of iterated and direct forecasts.
6. References
References for this Victoria’s Economic Bulletin research article.
7. Appendix
Appendix for this Victoria’s Economic Bulletin research article.
Updated