We build quantile-regression density forecasts for UK inflation and GDP growth and compare them with the Bank of England's fan charts.
We propose a correct specification test for path density forecasts that accounts for multiple horizons, and apply it to the Bank of England fan charts.
Nowcasting refers to the “forecast” of the current (“now”) state of the economy. This is necessary as key economic variables are often published with a significant delay of over a month. The nowcasting literature has arisen to address the need to have fast, reliable estimates of delayed economic indicators. The path signature is a mathematical object which captures geometric properties of sequential data; it naturally handles missing data from mixed frequency and/or irregular sampling – issues often encountered when merging multiple data sources – by embedding the observed data in continuous time. Calculating path signatures and using them as features in models have achieved state-of-the-art results in other fields such as finance, medicine, and cyber security. We look at the nowcasting problem by applying regression on signatures, a simple linear model on these nonlinear objects that we show subsumes the popular Kalman filter. We quantify the performance via a simulation exercise and application to US GDP growth, where in the latter we demonstrate no loss of performance compared with the dynamic factor model. By embedding discrete information in continuous time, this approach allows greater flexibility for future applications on data with complex sampling patterns.
Both monetary and macroprudential policymakers use conditional density forecasts of GDP to inform their policy decisions. The former tend to use ‘fan charts’ that convey uncertainty around central projections from linearised macroeconomic models. The latter draw on estimates of ‘growth-at-risk’, typically estimated using quantile-regression techniques, reflecting their focus on the tails of the GDP distribution. Focusing on the UK, we study how the fan charts constructed by the Bank of England’s Monetary Policy Committee compare to predictive densities derived from statistical growth-at-risk models. We find that GDP-at-risk models provide improved estimates of the left-tail of the GDP-growth distribution, in particular at medium-term horizons compared to the GDP fan charts. However, GDP-at-risk models generally perform worse than the fan charts at the centre of the distribution. Combining forecast densities in a parsimonious manner provides the best forecasts, with limited losses compared to optimal density combination methods. Doing so offers central banks the opportunity to improve GDP density forecasts, and unify the narrative provided by monetary and macroprudential policymakers about the economic outlook and uncertainty around it.
The combination of two or more density forecasts entails a long tradition the statistics and forecasting literature. However, little attention in econometrics has been given to the finite mixture distribution as a statistical model for combining density forecasts. Combination procedures based on a mixture density distribution are able to account for parameter uncertainty in addition to weights uncertainty, which are features normally not considered in the traditional two-step approaches. The paper proposes a comparison between combination approaches for density forecasting.