CARR Model

[Vik_pa]

Thanks Tom for the explanation.

I have another question. There is a Conditional autoregressive range model proposed by Chou (2005). "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model". In the same line another multivariate model was proposed as DCC CARR model. The paper is" Estimating Time-Varying Hedge Ratios with A Range-Based Multivariate Volatility Model".

Is it possible to model both CARR and DCC CARR in RATS?

Kind Regards

[TomDoan]

As he says, the CARR model is similar to the ACD model. There are several variants of ACD models in the tsayp270.rpf example. You should be able to tweak one of those.

[Vik_pa]

Thanks Tom.

I have check the EACD model and it is same as CARR model except that here the range is defined as duration. So CARR can be estimated with the help of EACD model.

This paper also mentioned that "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.6 This property is related to the above QMLE property by the observation of the equivalence of the exponential distribution's likelihood functions in CARR and ACD and the observation of the
normal density in GARCH. It is important to note that the direct application of QMLE will not yield consistent estimates for the covariance matrix of the parameters.
The standard errors of the parameters are consistently estimated by the robust method of Bollerslev and Wooldridge (1992)."

By this argument we can estimate it using

Code: Select all

GARCH(P=1,Q=1,NOMEAN) / SRANGE 

where srange is the square root of the range. But I am getting different results from these two methods. Can you please help me in understanding the difference between these two models.

Also, how to forecast the range using either of these models.

Thanks

[TomDoan]

Thanks Tom.

I have check the EACD model and it is same as CARR model except that here the range is defined as duration. So CARR can be estimated with the help of EACD model.

This paper also mentioned that "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.6 This property is related to the above QMLE property by the observation of the equivalence of the exponential distribution's likelihood functions in CARR and ACD and the observation of the
normal density in GARCH. It is important to note that the direct application of QMLE will not yield consistent estimates for the covariance matrix of the parameters.
The standard errors of the parameters are consistently estimated by the robust method of Bollerslev and Wooldridge (1992)."

By this argument we can estimate it using

Code: Select all

GARCH(P=1,Q=1,NOMEAN) / SRANGE 

where srange is the square root of the range. But I am getting different results from these two methods. Can you please help me in understanding the difference between these two models.

One is maximum likelihood, one is quasi-maximum likelihood. The latter is consistent, but not the same as ML.

Also, how to forecast the range using either of these models.

Is that a theoretical question? If you show me the formula, I can show you how to compute it using RATS.

[Vik_pa]

The reason I asked this becasue CARR and GARCH both are used for volatility forecasting. Like GARCH, the CARR also forecast the volatility as range is an estimator of the std deviation. So can I use the garchfore.src for forecasting purpose?

[TomDoan]

The reason I asked this becasue CARR and GARCH both are used for volatility forecasting. Like GARCH, the CARR also forecast the volatility as range is an estimator of the std deviation. So can I use the garchfore.src for forecasting purpose?

I don't know. That's a theoretical question. Read the papers carefully and see if they discuss how to do forecasting.