Estimating CARR Volatility Models with GARCH Methods

Summary

The document answers whether an R package is needed to estimate a conditional autoregressive range model. It describes the CARR approach as applying a GARCH-style specification to price ranges rather than to returns. The range is formed from the maximum and minimum prices observed during each measurement period, and its conditional scale is modeled using past ranges and past scale estimates.

The response says CARR’s quasi-maximum-likelihood estimation can be implemented through a suitably specified GARCH model, and suggests using a general GARCH package such as fGarch. This is a practical implementation direction rather than a package comparison or a validation study. The discussion relies on the questioner’s cited paper and a brief interpretation of its specification; it does not cover choosing model orders, distributional assumptions, data frequency, or diagnostics. Researchers should verify that a standard package’s parameterization matches the intended CARR specification before treating its estimates as equivalent.

Key ideas

• CARR models use price ranges as the time series input for volatility estimation.
• The range for a period can be measured as its maximum price minus its minimum price.
• A GARCH-style conditional scale equation can be fitted to ranges in place of returns.
• A general GARCH package may be adaptable, but its specification must match the CARR model.

Tags

# Is there any package in R for conditional autoregressive range model (CARR)?


# Is there any package in R for conditional autoregressive range model (CARR)?












I am working on a project which requires volatility estimation using range based volatility. Is there any package in R which helps me in estimating the CARR model proposed by Chou (2005).

## Answer by Stefan Voigt (score 1, accepted)

https://quant.stackexchange.com/a/22792

Welcome to quant.SE! I do not have specific experience with the CARR Model, however, I had a short look in the paper you mentioned: As far as I understand the model specification you just implement a GARCH(p,q) estimation for the range $R_t:=\max{P_\tau}-\min{P_\tau}$ where $\tau=t-1,t-1+\frac{1}{n},\dots,t$ where $n$ is the number of intervals used in measuring the price. Instead of implementing GARCH for the returns $r_t$ you just compute the same for $$R_t=\lambda_t\varepsilon_t\\\lambda_t=\omega+\sum\alpha_iR_{t-1}+\sum\beta_i\lambda_{t-1}$$. This is in line with Section 1.2 of the original paper, stating:

> A convenient property for CARR is the ease of estimation. Specifically, the QMLE estimation of the CARR model can be obtained by estimating a GARCH model with a particular specification: specifying a GARCH model for the square root of range without a constant term in the mean equation

Therefore, to answer your question: Just compute a time-series $R_t$ of ranges and then run any package computing GARCH for you, for example fGarch.

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