Single-season heteroscedasticity in time series

We consider seasonal time series in which one season has variance that is different from all the others. This behaviour is evident in indices of production where variability is highest for the month with the lowest level of production. We show that when one season has different variability from others there are constraints on the seasonal models that can be used; neither dummy nor trigonometric models are effective in modelling this type of behaviour. We define a general model that provides an appropriate representation of single-season heteroscedasticity and suggest a likelihood ratio test for the presence of periodic variance in one season.