Abstract
This article aims to estimate the Conditional Autoregressive Range Model CARR (p, q) by the use of three different procedures: The ARMA model (p, q) using least squares estimators (MCO), the GARCH model (p, q) using Quasi-Maximum Likelihood Estimators (QMLE) and the GARCHX model (p, q) using Maximum Likelihood Estimators (MLE).
The usage of these three procedures is in function of the considerations made on the probability distribution of errors and the estimators’ properties that are to be emphasized. At a second stage, instead of daily observations, estimations of the same models were made on a, weekly, fortnightly, and monthly observation basis. Finally we demonstrate that the best results are obtained through the ARMA (p, q) and GARCHX models (p, q), regardless of whether the extreme value ranges come from daily, weekly, fortnightly or monthly observations.
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