Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

BIS Working Papers  |  No 667  | 
31 October 2017



Forward-looking monetary policy relies not only on forecasts of variables like economic growth and inflation, but must also assess and communicate the uncertainty around those forecasts. Often, forecast uncertainty is depicted with 'fan' charts that predict a range in which future data are likely to fall.

Surveys regularly provide data on economic forecasts. But survey respondents do not always provide quantitative measures of forecast uncertainty. Instead, uncertainty can be gauged based on past forecast performance. When doing so, the distribution of forecast errors is typically assumed to have remained unchanged for at least a decade. Fan charts are then slow to adapt when the size of the errors shifts, as it did during the 1980s or the recent financial crisis.


We model uncertainty around survey forecasts. Our model tracks changes in the range of likely outcomes better than an approach that simply averages over the last two decades or so. A simple average puts equal weight on all data points in a given subsample, dropping some early data points which may be less relevant in assessing forecast uncertainty later on. Our model considers all the data available from a given survey, but weighs them differently. Our estimates put more weight on the recent past than a simple average over 15 years.


We apply our model to forecasts for economic growth, unemployment, inflation and nominal short-term interest rates from the Federal Reserve Bank of Philadelphia's Survey of Professional Forecasters. Fan charts from our model predict the range of future forecast errors better than the simple-average approach. We find similar results when we apply our model to staff forecasts published by the Federal Reserve.



We develop uncertainty measures for point forecasts from surveys such as the Survey of Professional Forecasters, Blue Chip, or the Federal Open Market Committee's Summary of Economic Projections. At a given point of time, these surveys provide forecasts for macroeconomic variables at multiple horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon speci cation of stochastic volatility. Compared to constant-variance approaches, our stochastic-volatility model improves the accuracy of uncertainty measures for survey forecasts.

JEL classification: E37, C53

Keywords: stochastic volatility, survey forecasts, fan charts