  Functional time series data frequently appears in economic applications,
where the functions of interest are subject to some shape constraints,
including monotonicity and convexity, as typical of the estimation of the
Lorenz curve. This paper proposes a state-space model for time-varying
functions to extract trends and serial dependence from functional time series
while imposing the shape constraints on the estimated functions. The function
of interest is modeled by a convex combination of selected basis functions to
satisfy the shape constraints, where the time-varying convex weights on simplex
follow the dynamic multi-logit models. For the complicated likelihood of this
model, a novel data augmentation technique is devised to enable posterior
computation by an efficient Markov chain Monte Carlo method. The proposed
method is applied to the estimation of time-varying Lorenz curves, and its
utility is illustrated through numerical experiments and analysis of panel data
of household incomes in Japan.
