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.

翻译：函数时间序列数据在计量经济学分析中频繁出现，其中所关注的函数通常受到某些形状约束，包括单调性和凸性，这在洛伦兹曲线的估计中尤为典型。本文提出了一种用于时变函数的状态空间模型，旨在从函数时间序列中提取趋势和序列依赖性，同时对估计函数施加形状约束。所关注的函数通过选定基函数的凸组合进行建模，以满足形状约束，其中单纯形上的时变凸权重遵循动态多元Logit模型。为了能够通过高效的马尔可夫链蒙特卡洛方法进行后验计算，本文针对该模型的复杂似然函数设计了一种新颖的数据增强技术。所提出的方法被应用于时变洛伦兹曲线的估计，并通过数值实验和对日本家庭收入面板数据的分析，展示了其实用性。