Threshold Asymmetric Conditional Autoregressive Range (TACARR) Model

Abstract

This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) model for analyzing the daily price ranges of financial assets. The proposed formulation assumes that the conditional expected range switches between two regimes, representing upward and downward market states, with the disturbance distribution also allowed to vary across regimes. A self-adjusting threshold component, determined by past values of the series, is used to identify the prevailing market regime. In this way, the model is able to capture asymmetric and heteroscedastic volatility behavior in financial markets. The TACARR model is designed to address several limitations of existing price range models, including the Conditional Autoregressive Range (CARR), Asymmetric CARR (ACARR), Feedback ACARR (FACARR), and Threshold Autoregressive Range (TARR) models, with and without exogenous variables. Model parameters are estimated using the maximum likelihood (ML) method, and a simulation study shows that the proposed estimation procedure performs well. The empirical performance of the TACARR model under several distributional assumptions is evaluated using IBM stock and S&P 500 index, and the results show that it serves as a flexible and competitive alternative to existing models for both in-sample fitting and out-of-sample volatility forecasting.