State-Space Modeling of Shape-constrained Functional Time Series

Functional time series data frequently appears in econometric analyses, 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. To enable posterior computation by an efficient Markov chain Monte Carlo method, a novel data augmentation technique is devised for the complicated likelihood of this model. 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.