DOI: https://doi.org/10.71734/DP–2025–35

Non-technical summary

Research Question

This paper addresses the challenge of incorporating conditions on annual growth rates into forecast models that work with higher-frequency data, such as quarterly or monthly figures. Specifically, it examines how to integrate these annual growth conditions into vector autoregressive (VAR) models, which often use logarithms or differences of logarithms to handle economic data like GDP or prices. The main question is how to ensure that the forecasts produced by these models can account for expected or desired annual growth rates, even though the models themselves operate on a different timescale and mathematical basis.

Contribution

To solve this problem, the paper uses a method that approximates the annual growth rate by linearizing it as a function of the VAR model variables. This linearization enables the application of standard forecasting techniques while incorporating conditions on annual growth rates. Since this is an approximation, a discrepancy arises between the imposed conditions and the model's output. To minimize this approximation error, the paper proposes an iterative process that adjusts the conditions repeatedly until the model's results closely match the desired annual growth rates.

Results

By employing the linear approximation and iterative adjustment process, the paper effectively integrates conditions on annual growth rates into the VAR forecasting framework. This approach reduces the approximation error and ensures that the imposed conditions closely align with the forecasted outcomes. The method enhances the practical applicability of VAR models in economic forecasting, particularly when aligning higher-frequency models with annual projections from official sources such as government agencies or central banks.

Mokinski, F., M. Roth (2025), Forecasting with log-linear (S)VAR-models: Incorporating annual growth rate conditions, Bundesbank Discussion Paper, No 35/2025.