The effect of conditional heteroskedasticity on common statistical procedures for means and variances

Summary: Commonly used standard statistical procedures for means and variances (suchas the t–test for means or the F–test for variances and related confidence procedures) requireobservations from independent and identically normally distributed variables. Theseprocedures are often routinely applied to financial data, such as asset or currency returns,which do not share these properties. Instead, they are nonnormal and show conditionalheteroskedasticity, hence they are dependent. We investigate the effect of conditionalheteroskedasticity (as modelled by GARCH(1,1)) on the level of these tests and the coverageprobability of the related confidence procedures. It can be seen that conditionalheteroskedasticity has no effect on procedures for means (at least in large samples). Thereis, however, a strong effect of conditional heteroskedasticity on procedures for variances.These procedures should therefore not be used if conditional heteroskedasticity is prevalentin the data.*We are grateful to the referees for their useful and constructive comments.