Seasonality in large-scale macroeconometric models

Abstract

Macroeconomic indicators are typically appraised in seasonally adjusted form, and forecasts are often presented in a similar way (as annual changes, for example). Moreover, the quarterly macroeconomic models used in forecasting are commonly estimated from seasonally adjusted data. Nevertheless, these models can generate forecasts with seasonal patterns, and this paper assesses the cause and cure of this phenomenon. It is found that forecast seasonality is induced by seasonality in the various inputs: exogenous variables, residual adjustments, the dynamic specification of certain equations, and annual changes in policy variables. Series changing annually but observed quarterly are termed ‘intercalated series’, and are simple examples of periodic processes. Forecast seasonality can be removed by appropriate adjustment of all these inputs. Models containing explicit future expectations variables solved in a model-consistent manner are also considered: numerical sensitivity to the terminal quarter may result from terminal conditions that require adjustment when seasonality is present.