Dissecting models' forecasting performance

The fact that the predictive performance of models used in forecasting stock returns, exchange rates, and macroeconomic variables is not stable and varies over time has been widely documented in the forecasting literature. Under these circumstances excessive reliance on forecast evaluation metrics that ignores this instability in forecasting accuracy, like squared errors averaged over the whole forecast evaluation sample, masks important information regarding the temporal evolution of relative forecasting performance of competing models. In this paper we suggest an approach based on the combination of the Cumulated Sum of Squared Forecast Error Differential (CSSFED) of Welch and Goyal (2008) and the Bayesian change point analysis of Barry and Hartigan (1993) that tracks the contribution of forecast errors to the aggregate measures of forecast accuracy observation by observation. In doing so, it allows one to track the evolution of the relative forecasting performance over time. We illustrate the suggested approach by using forecasts of the GDP growth rate in Switzerland.