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CPS2135 Sumonkanti Das et al.
the period 1999-2017 serve as input for developing multilevel time series
models to predict more smooth and robust trend series.
Over the period of 1999-2017, there were two redesigns in the DTS: one in
2004 when the survey data collection was transferred to another agency and
another one in 2010 when Statistics Netherlands restarted data collection. The
period 1999-2003 is referred to as OVG, 2004-2009 as MON and 2010-2017
as OViN. These are abbreviations of Dutch names for the DTS used in the
different periods. Discontinuities due to redesigns are sometimes masked by
the volatility of the point estimates at detailed level. Some discontinuities are
clearly visible at aggregate levels and need to be accounted for in the model
development for trend estimation.
The direct estimates with their standard errors are available for all 504
domains, however there are some structural zeroes (such as motive work and
mode car driver for children) for which the estimates are identically zero.
Additionally, there are many other domains with zero direct estimates, but
they are zero only coincidentally due to no observations of journeys in such
domains in a particular year. Since the sample sizes of some domains are too
small to produce reliable direct point estimates, the variance estimates are also
unstable. In addition, for some domains point estimates are found unreliable
for the year 2009 due to issues with the field work in the last MON year. These
estimates behave as outliers in the time series data of 1999-2017. To obtain
sufficiently stable variance approximations for the point estimates, required
for time series modeling, the direct variance estimates are modeled by a GVF
following Wolter (2007) to construct stable variance approximations for the
direct variance estimates.
In Bollineni-Balabay et al. (2017) structural time series models and
multilevel time series models were used to estimate trends for mobility
(average distance traveled pppd) by journey motive and transportation mode.
They found the differences between the two modeling frameworks were
generally small. However, Boonstra and van den Brakel (2016) found multilevel
time series models in a hierarchical Bayesian formulation have some
advantages in terms of flexibility and computational efficiency. Therefore, time
series multilevel model has been considered in this study to borrow strength
over time and space while accounting for discontinuities and outliers.

2. Methodology
2.1 Input estimates
The direct estimates are obtained by the generalized regression estimator
(Särndal et al., 1992). Standard errors of the direct estimates are approximated
by Taylor linearization, and account for weighting and unequal inclusion
ˆ
probabilities. Let Y it denote the direct estimate of the average number of
journey parts pppd for year t, t = 1999,...,2017 and domain i, i = 1,...,504.
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