The Hyperbolic Conditional Autoregressive Range (HYCARR) Model

• Activity Number: 92 - Time Series and Finance
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Isuru Ratnayake* and V A Samaranayake
• Companies: Kansas University Medical Center and Missouri University of Science and Technology
• Keywords: long memory; range based model; CARR process; non negativity ; moment properties; hyperbolic function

Abstract

This paper proposes the Hyperbolic Conditional Autoregressive Range (HYCARR) model to analyze the long-memory or long-term dependencies of the price range of a financial asset. The Conditional Autoregressive Range (CARR) model explains the current conditional mean of a price ranges as a function of past conditional mean price range values and past prices range data. However, the Auto covariance Function (ACF) of the price range series exhibits statistically significance correlation up to far end, which indicates the presence of long-memory properties in the finance data. In this paper long-memory properties in the price range data are examined. The standard CARR process accounts for short-memory properties in the conditional price range data. The long-memory behavior in the return-based models were well explained in the Integer GARCH (IGARCH), Fractionally IGARCH (FIGARCH) and Hyperbolic GARCH (HYGARCH) studies. This paper mainly focuses on discussing the gap knowledge exists in the long-memory properties in the range-based models. Further, the paper examines the non-negativity conditions of the HYCARR model for the conditional mean range term are derived. The Maximum Likelihood Estimation (MLE) technique is discussed to estimate the proposed model. The simulation study is carried out to estimate the finite sample performance of the proposed HYCARR model. The empirical study of the HYCARR model is illustrated by usingS&P500 index data.