Real-Time Inflation Forecast Densities from Ensemble Phillips Curves

Abstract

A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock and Watson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries.

Real‐time inflation forecast combination for time‐varying coefficient models

“…In the present study, we use real-time data in the forecasting exercise instead of heavily revised data. There has already been much Bayesian work studying real-time macroeconomic variable forecasting, such as forecasts using Bayesian vector autoregressive models (Clark, 2011), forecasts of inflation and the output gap (Garratt, Mitchell, Vahey, & Wakerly, 2011), UK monetary aggregates (Garratt, Koop, Mise, & Vahey, 2009), inflation forecasts by Bayesian model averaging (Groen et al, 2013), and forecasts of macroeconomic variables by a copula model with asymmetric margins (Smith & Vahey, 2016). The present study follows these pioneer studies and employs both Bayesian estimation and real-time data to study inflation.…”

“…We compute forecast combinations by weighting the forecasts from different models. Specifically, recursive weights based on historical forecast performance are used for model averaging forecasts (e.g., Garratt et al, 2011;Jore et al, 2010), so that the model averaging weights are evaluated repeatedly by the following vintages.…”

Combining density forecasts using focused scoring rules

“…The second scheme, adopted from Jore, Mitchell, and Vahey (2010), assigns weights to the various individual density forecasts based on their relative average scores. Garratt, Mitchell, Vahey, and Wakerly (2011) and Aastveit, Gerdrup, Jore, and Thorsrud (2014) show that these recursive weighting schemes perform well when combining density forecasts of inflation and GDP respectively. The latter study also finds that this scheme performs better in terms of point forecast evaluation than standard point forecast combinations.…”

The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions

“…If we can show that the real-time signal extraction error process {ε t } depends only on future innovations, then by the causality of {X t } the error process must be uncorrelated with X Now by applying the method of proof in Proposition 2, we obtain the formula (19) for Φ. Plugging back into D Ψ (ϑ, G) yields the minimal value (20). 2…”