• Document: Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models
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University of Wollongong Research Online Centre for Statistical & Survey Methodology Faculty of Engineering and Information Sciences Working Paper Series 2010 Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models C. Birrell University of Wollongong, cbirrell@uow.edu.au D. G. Steel University of Wollongong, dsteel@uow.edu.au Y. X. Lin University of Wollongong, yanxia@uow.edu.au Recommended Citation Birrell, C.; Steel, D. G.; and Lin, Y. X., Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 01-10, 2010, 23p. http://ro.uow.edu.au/cssmwp/48 Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: research-pubs@uow.edu.au Centre for Statistical and Survey Methodology The University of Wollongong Working Paper 01-10 Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models Carole L. Birrell, David G. Steel and Yan-Xia Lin Copyright © 2008 by the Centre for Statistical & Survey Methodology, UOW. Work in progress, no part of this paper may be reproduced without permission from the Centre. Centre for Statistical & Survey Methodology, University of Wollongong, Wollongong NSW 2522. Phone +61 2 4221 5435, Fax +61 2 4221 4845. Email: anica@uow.edu.au 1 Seasonal Adjustment of an Aggregate Series using Univariate and Multivariate Basic Structural Models Carole L. Birrell, Centre for Statistical and Survey Methodology School of Mathematics and Applied Statistics University of Wollongong, 2522 NSW, Australia Email: cbirrell@uow.edu.au David G. Steel Centre for Statistical and Survey Methodology School of Mathematics and Applied Statistics University of Wollongong, 2522 NSW, Australia Email: dsteel@uow.edu.au Yan-Xia Lin Centre for Statistical and Survey Methodology School of Mathematics and Applied Statistics University of Wollongong, 2522 NSW, Australia Email: yanxia@uow.edu.au Abstract Time series resulting from aggregation of several sub-series can be seasonally adjusted directly or indirectly. With model-based seasonal adjustment, the sub- series may also be considered as a multivariate system of series and the analysis may be done jointly. This approach has considerable advantage over the indirect method, as it utilises the covariance structure between the sub-series. This paper compares a model-based univariate and multivariate approach to seasonal adjustment. Firstly, the univariate basic structural model (BSM) is applied directly to the aggregate series. Secondly, the multivariate BSM is applied to a transformed system of sub-series. The prediction mean squared errors of the seasonally adjusted aggregate series resulting from each method are compared by calculating their relative efficiency. Results indicate that gains are achievable using the multivariate approach according to the relative values of the parameters of the sub-series. AMS Subject Classification: 62M10, 91B84 Keywords: Seasonal adjustment, Basic structural model, Kalman filter, mul- tivariate time series, state space model. 1 Introduction Seasonally adjusted time series of economic and social data are important prod- ucts of many official statistical agencies. Data for a number of series is often collected, sometimes geographically or by industry, and then aggregated to ob- tain a total series. Seasonal adjustment of this aggregated series, as well as the sub-series (or cross-sectional series), is usually required for publication. Given that seasonal adjustment involves estimating and removing the seasonal effects Seasonal Adjustment of an Aggregate Series 2 of the series, it is important that the method employed produces accurate esti- mates of the seasonal components. When the seasonal component of a series is estimated from the aggregated series and then removed, the process is called direct seasonal adjustment. Al- ternatively, if each of the sub-series is seasonally adjusted separately, and then summed to obtain the aggregated seasonally adjusted series, the process is called indirect seasonal adjustment. Both direct and indirect seasonal adjustment em- plo

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