Modeling the Variance of Return Intervals Toward Volatility Prediction

Interval‐valued time series has been attracting increasing interest. There have been fruitful results on mean models, but variance models largely remain unexploited. In this article, we propose a conditional heteroskedasticity model for the return interval process, which aims at capturing the underlying variance structure. Under the general framework of random sets, the model properties are investigated. Parameters are estimated by the maximum likelihood method, and the asymptotic properties are established. Empirical application to stocks and financial indices data sets suggests that our model overall outperforms the traditional generalized autoregressive conditional heteroskedasticity for both in‐sample estimation and out‐of‐sample prediction of the volatility.