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A Vector Autoregressive Moving Average Model for Interval-Valued Time Series Data

Ai Han, Yongmiao Hong (), Shouyang Wang and Xin Yun

A chapter in Essays in Honor of Aman Ullah, 2016, vol. 36, pp 417-460 from Emerald Publishing Ltd

Abstract: Abstract Modelling and forecasting interval-valued time series (ITS) have received increasing attention in statistics and econometrics. An interval-valued observation contains more information than a point-valued observation in the same time period. The previous literature has mainly considered modelling and forecasting a univariate ITS. However, few works attempt to model a vector process of ITS. In this paper, we propose an interval-valued vector autoregressive moving average (IVARMA) model to capture the cross-dependence dynamics within an ITS vector system. A minimum-distance estimation method is developed to estimate the parameters of an IVARMA model, and consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. A two-stage minimum-distance estimator is shown to be asymptotically most efficient among the class of minimum-distance estimators. Simulation studies show that the two-stage estimator indeed outperforms other minimum-distance estimators for various data-generating processes considered.

Keywords: Asymptotic efficiency; interval vector-valued time series; interval-valued data; minimum-distance estimation; vector autoregressive moving average interval models; C3; C32 (search for similar items in EconPapers)
Date: 2016
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