# An interval-valued GARCH model for range-measured return processes

## TL;DR

This paper introduces an interval-valued GARCH model that captures the information in range-measured returns, improving volatility estimation and prediction over traditional GARCH models.

## Contribution

It proposes a novel interval-valued GARCH model for range data, with theoretical properties and empirical validation on financial data.

## Key findings

- Int-GARCH outperforms traditional GARCH in volatility prediction
- Model effectively captures information in range-measured returns
- Parameters estimated with maximum likelihood, with established asymptotic properties

## Abstract

Range-measured return contains more information than the traditional scalar-valued return. In this paper, we propose to model the [low, high] price range as a random interval and suggest an interval-valued GARCH (Int-GARCH) model for the corresponding range-measured return process. 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 Int-GARCH model overall outperforms the traditional GARCH for both in-sample estimation and out-of-sample prediction of volatility.