Trading days, seasonal unit root, and variance change

A time series model is developed for the Brazilian index of total industrial production, including a trading days effect well accounted for by only one variable. Estimation using the exact likelihood function produces a unitary MA seasonal root and thus a common factor in the equation. This is dealt with first by using dummies and later by transforming the original data using difference equation solution properties to obtain a simplified model. The residuals show a variance change at a well defined point and this is confirmed with an F test. A new simplified model is built that allows for a variance change, and after a suitable data transformation it is reestimated and its forecasting performance tested.