Multivariate State Space Approach to Variance Reduction in Series with Level and Variance Breaks Due to Survey Redesigns

Abstract

Statistics Netherlands applies a design-based estimation procedure to produce road transportation figures. Frequent survey redesigns caused discontinuities in these series which obstruct the comparability of figures over time. Reductions in the sample size and changes in the sample design resulted in variance breaks and unacceptably large sampling errors in the recent part of the series. Both problems are addressed and solved simultaneously. Discontinuities and small sample sizes are accounted for by using a multivariate structural time series model that borrows strength over time and space. The paper illustrates an increased precision when we move from univariate models to a multivariate model where the domains are jointly modelled. This increase is especially significant in the most recent period when sample sizes become smaller, with standard errors of the design-based estimator of the target variables being reduced by 40-70% with the model-based approach.

Small Area Estimation with State Space Common Factor Models for Rotating Panels

“…In this application, model-based estimates are also produced at the national level. Bollineni-Balabay et al (2016) proposed to derive model-based estimates at the national level from the results that are obtained from a multivariate model for the domains. Another alternative is to apply a Lagrange function to benchmark model-based estimates at the national level with model-based estimates for the underlying domains.…”

Multilevel Hierarchical BayesianVersusState Space Approach in time Series Small Area Estimation: the Dutch Travel Survey

“…Here, the last formulation is preferred because of its well-known flexibility and parsimony (Durbin andKoopman (2012), chapter 3, andHarvey (2001)). This application, as well as that in Bollineni-Balabay et al (2016), provides evidence for data overfitting when the other two specifications of the stochastic trends were applied. Therefore, only the smooth trend model is considered in this paper.…”

“…This application, as well as that in Bollineni‐Balabay et al . (), provides evidence for data overfitting when the other two specifications of the stochastic trends were applied. Therefore, only the smooth trend model is considered in this paper.…”

“…Time series extensions of the Fay-Herriot model can be found in Rao and Yu (1994), Datta et al (1999) and You (2008). For small area applications modelled with structural time series (STS) techniques, see Pfeffermann (1991), Pfeffermann and Bleuer (1993), Pfeffermann and Tiller (2006), Pfeffermann et al (2014), Krieg and Van den Brakel (2012), Van den Brakel and Krieg (2016) and Bollineni-Balabay et al (2016). Furthermore, time series models can help to compare figures before and after survey redesigns by estimating level breaks.…”

Changing Industrial Classification to SIC (2007) at the UK Office for National Statistics

“…A model-based approach to this involves the Kalman filter, and Bollineni-Balabay et al (2016) give a complex example covering multiple changes, which demonstrates the efficacy of the procedure in more complex cases than reclassification.…”