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TIME SERIES MODELS FOR SMALL AREA ESTIMATION

There is a continuing demand for the Australian Bureau of Statistics (ABS) to provide statistics for small areas. The ABS has both good knowledge and practical experience with cross-sectional small area models. However, there are needs and opportunities that now motivate us to explore methods that can also borrow strength across time. There are current opportunities presented by existing ABS repeated surveys, in particular the Labour Force Survey with its rotating panel design. Future opportunities will arise for any household surveys that transition from periodic to continuous collection, so that sample is no longer concentrated in an occasional large survey but spread evenly over time. In response, we initiated a research project to investigate the application of time series methods for small area estimation.

In the literature two broad approaches are described; temporal multilevel models and structural time series models (Bollineni-Balabay et al, 2016). These methods were applied to the Australian Labour Force Survey to obtain and compare modelled estimates for Labour Force dissemination regions. For the structural time series approach multivariate models were fit, with borrowing strength over regions achieved by allowing potential non-zero correlations between the disturbances of the trend and seasonal components of the model. The Rao-Yu multilevel model (Rao and Yu, 1994) was implemented and estimated as a state space model with unemployment benefits data (provided by the Department of Social Services) used as a regression covariate. Estimation for the models was performed using the Dynamic Linear Model package in R.

The results may be considered preliminary in nature. However, strong improvements in the variances of the modelled estimates compared to the direct estimates were clear, under both the multilevel and structural time series approaches. The work was presented at the November Methodology Advisory Committee meeting. Further work is planned to refine the models, including the incorporation of a seasonal component into the Rao-Yu model, and fitting of Seemingly Unrelated Time Series (SUTSE) bivariate models that incorporate the unemployment benefits data.

Reference

Bollenini-Ballabay, O., van den Brakel, J., Palm, F. and Boonstra, H. (2016) 'Multilevel hierarchical Bayesian vs. state space approach in time series small area estimation: the Dutch travel survey'. Discussion paper, Statistics Netherlands.

Rao, J.N.K. and Yu, M. (1994) 'Small area estimation by combining time series and cross-sectional data' Canadian Journal of Statistics, 22, pp. 511-528.