Modelling Business Cycle Nonlinearity in Conditional Mean and Conditional Variance: Some International and Sectoral Evidence

This paper tests for the presence of output mean and variance nonlinearities in international industrial production and UK and US sectoral production growth rates using ARMA–GQARCH, bilinear (BL) and joint BL–GQARCH models. ARMA–GQARCH models confirm the presence of asymmetric variance effects in Italian, UK and US industrial production and in all sectors other than US nondurables, and such that the conditional variance of output is increased following negative shocks. BL models are identified for German, Italian and US industrial production and US manufacturing, while BL–GQARCH models of joint non‐linearity in both conditional mean and conditional variance are also found to hold for US industrial production and manufacturing. Moreover, with the exception of Italy, all BL and BL–QARCH models provide superior out‐of‐sample mean forecasts relative to forecasts from both naïve models and models of the ARMA–GQARCH class.