Uncertainty And Risk Analysis Of Macroeconomic Forecasts: Fan Charts Revisited

Since 1996 the Bank of England (BoE) has been publishing estimates of probability distribution of the future outcomes of inflation and output growth. These density forecasts, known as "fan charts", became very popular with other central banks (e.g. Riskbank) as a tool to quantify uncertainties and risks of conditional point forecasts. The BoE's procedure is mainly a methodology to determine the distribution of a linear combination of independent random variables. In this article we propose an alternative methodology that addresses two issues with the BoE procedure that may affect the estimation of the densities. The first issue relates to a statistical shortcut taken by the BoE that implicitly considers that the mode of the linear combination of random variables is the (same) linear combination of the modes of those variables. The second issue deals with the assumption of independence, which may be restrictive. An illustration of the new methodology is presented and its results compared with the BoE approach.