Estimation of the variances of X-11 ARIMA seasonally adjusted estimators for a multiplicative decomposition and heteroscedastic variances

Extensions of a method proposed by Pfeffermann (1993, J. Time Series Analysis, 15, 85-116) for estimating the variances of X-11 ARIMA estimators are considered. The extensions include the use of a multiplicative decomposition and the allowance for changes in the variances and covariances of the error terms. We also examine how the variances of the seasonally adjusted estimators are affected by the identification and estimation of ARIMA models used for extrapolating the original series and by the identification and gradual replacement of extreme observations.