MATLAB: Do I obtain different results fitting a GARCH process using the UGARCH and GARCHFIT functions

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I have tried to use the UGARCH function in the Financial Toolbox and the GARCHFIT function in the GARCH Toolbox to fit a GARCH process. However, the two functions return different results despite the same data being used.

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The UGARCH and GARCHFIT functions implement the GARCH model fitting process differently. The two functions use different optimization objective functions in their implementations. Therefore, although both functions provide the same functionality, the differences between their implementations may result in different results at times. However, most of the time, their results should be similar.

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MATLAB: Do I get different results when using the ‘ADFTEST’ and ‘PARCORR’ functions in the Statistics Toolbox 7.4 (R2010b)

The issue here is that PARCORR includes a constant in its OLS regression estimates of the partial autocorrelation coefficients, per references such as Box & Jenkins. So, we should compare the results of ADFTEST using the 'ARD' model instead of 'AR' as follows:

[h1_cpi,pVal1_cpi,stat,~,reg1_cpi]= adftest(data,'model','ard','lags',0);

When the constant (drift term) is included in ADFTEST, and the number of lags of differenced data is 0 (i.e., the simple DF test), then the results should match.

MATLAB: How to assess adequacy of fitted GARCH model

When you fit an ARIMA model to a time series the residuals should exhibit no heteroscedasticity. If they do you fit an ARIMA/GARCH model. The model is adequate if the residuals have no significant autoregressive conditional hetereoscedasticity once they have been standardized by their conditional volatility. That is how you assess the adequacy of a GARCH model according to one of my textbooks. In addition you can do a visual inspection. Plot the residuals and the GARCH volatility and check if the model is capable of capturing volatility clustering.

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Related Solutions

MATLAB: Do I get different results when using the ‘ADFTEST’ and ‘PARCORR’ functions in the Statistics Toolbox 7.4 (R2010b)

MATLAB: How to assess adequacy of fitted GARCH model

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