Improving Seasonal Adjustment by Accounting for Sampling Error Correlation Using State Space Models

South Australian SSA 21 March 2018 Meeting with Julian Whiting

Speaker Julian Whiting

Julian began his talk by describing how the Australian Bureau of Statistics (ABS) produces a large number of time series of economic indicators, and many of these series are sample survey estimates.  Sampling error can have a particularly noticeable impact on time series of survey estimates relating to small populations, such as labour force or retail sales within the smaller States or Territories.  The effects of sampling error are currently not taken into account by the seasonal adjustment process used at the ABS, which is the non-parametric X-11 filter-based method also used by many other National Statistical Offices.

The rotating panel sample designs adopted for many sample surveys results in a degree of correlation between the sampling error contribution from period to period.  This persistence in sampling error affects estimation of the series trend, which is a construct intended to capture the underlying level of the series.  The fact that the sampling error is not random noise but has some structure gives promise that the contribution of sampling error can be distinguished from random irregular influences on the time series, thereby allowing the contribution of sampling error to be estimated.

Julian outlined how the sampling error contribution can estimate by fitting a basic structural model (BSM) to the observed data.  The model describes a time series as the sum of trend, seasonal, irregular and sample error components, where each component has its own defined structure.  Knowledge of the survey sample design is used to specify the sampling error model structure and estimate the model’s parameters.

Fitting the BSM to the observed time series produces estimates of the trend, seasonal, irregular and sample error components, and one output strategy would be to publish trend and seasonally-adjusted series from the fitted values of the relevant components.  The seasonal adjustment method which Julian has investigated has been to apply the X-11 seasonal adjustment method to a time series in which the modelled sample error estimate has been removed from the observed time series.

Julian finished his talk by discussing the simulation studies used to investigate the properties of the method.  The simulations showed the method has promise: on average it noticeably improved estimation of period-to-period change and slightly improved estimates of the series level, and the method appears sufficiently robust when there are sudden changes in the underlying time series.  The method is also not particularly sensitive to misspecification of the sampling error component.  Further research work is required on issues which would need to be addressed to allow practical application, for example ensuring coherent correction for sampling error across a suite of time series related through an aggregation hierarchy.

Shahid Ullah

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