  Traditional credibility analysis of risks in insurance is based on the random
effects model, where the heterogeneity across the policyholders is assumed to
be time-invariant. One popular extension is the dynamic random effects (or
state-space) model. However, while the latter allows for time-varying
heterogeneity, its application to the credibility analysis should be conducted
with care due to the possibility of negative credibilities per period [see
Pinquet (2020a)]. Another important but under-explored topic is the ordering of
the credibility factors in a monotonous manner -- recent claims ought to have
larger weights than the old ones. This paper shows that the ordering of the
covariance structure of the random effects in the dynamic random effects model
does not necessarily imply that of the credibility factors. Subsequently, we
show that the state-space model, with AR(1)-type autocorrelation function,
guarantees the ordering of the credibility factors. Simulation experiments and
a case study with a real dataset are conducted to show the relevance in
insurance applications.
