Nonparametric estimation and forecasting of interval-valued time series regression models with constraints

Nowadays information technology advances allow the collecting and storage of large complex data sets in many areas. Modeling and forecasting interval-valued time series (ITS) has drawn much attention over the last two decades because interval-valued observations contain more information than point-valued observations over the same period and remove undesirable noises in high-frequency data. However, most work mainly focuses on modeling a linear univariate ITS or bivariate point process. This paper proposes nonparametric regression models for interval-valued time series with imposing constraints, e.g., monotonicity. This setting with a monotonic constraint is consistent with the existing literature, which focuses on incorporating valuable empirical information in modeling and forecasts. Two constraint estimators are developed and asymptotic properties are established. Monte Carlo simulation is conducted to show the finite sample performance. An empirical application to equity premium documents that the proposed model yields a better forecast performance than some popular models in the literature.