Affiliations: National Institute for Applied Statistics Research Australia (NIASRA), School of Mathematics and Applied Statistics, University of Wollongong, NSW, Australia
Corresponding author: Carole L. Birrell, National Institute for Applied Statistics Research Australia (NIASRA), School of Mathematics and Applied Statistics, University of Wollongong, 252 NSW, Australia. E-mail:[email protected]
Abstract: An aggregate series is a time series resulting from the aggregation of two or more sub-series.
Two model-based approaches to seasonal adjustment of the aggregate series include
a univariate and multivariate basic structural model. In a previous study , the variance of
the seasonally adjusted series for the two approaches were compared using a range
of true parameter values for a fixed length series.
This paper compares the model-based univariate and multivariate approaches
for different series lengths using the estimated parameters.
A simulation study compares two outcomes: the accuracy of the estimated parameters
of the aggregate series, and the naïve bias in the prediction error variance.
The results show that for the two cases studied,
the use of the multivariate approach in the
estimation of parameters improves the accuracy of the parameter
estimates of the aggregated series. This was
especially true for short to medium length time series. The
relative efficiencies of the seasonally adjusted aggregated series
also showed good gains for the multivariate model.
For one of the cases, there was a substantial
decrease in the naïve bias with the use of the multivariate
model. Bias correction is also discussed for the two approaches.
Keywords: Basic structural model, bootstrap correction, kalman filter, multivariate time series, naïve bias, parameter estimation, seasonal adjustment, state space model