How to compare GARCH volatility forecast performance?
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调研方向
Start with the linked volatility-forecasting documentation and the arch_model / ARCHModelForecast APIs named in the issue. Clarify what variance represents and what target the author should use for evaluating forecasts; done means the three questions about interpretation, MSE, and the reported fit are answered.
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描述
I have a question regarding the evaluation of volatility forecasts using the arch_model class. I am very new, so I sincerely apologise if this is obvious, or if this is the wrong place to ask.
I want to forecast the daily volatility (for a test set of roughly 1000 obs) of stock returns using a GARCH model, and concretely using the arch package. After doing so, I want to measure the forecasting performance using the mean squared error.
I construct a model using mean adjusted and scaled returns arch_model(x_var, mean="Zero", vol="Garch", p=1, q=1) and I fit the model using model.fit(last_obs="2018-07-03", update_freq=10) to produce a fixed window forecast as in the tutorial in the documentation.
What I am having trouble with is:
- Correctly understanding the
ARCHModelForecastobject. Is it correct that thevarianceattribute is the prediction for the daily volatility? - If yes, what value do I compare it to to calculate the MSE? My understanding for GARCH models was that you use squared returns as a proxy for volatility, but my model forecasts are nowhere near the returns, squared returns, or any other feature I have in my data set. Is it correct that I would compare the forecast values to the squared returns at the according time step to evaluate prediction performance?
- If yes, is the model I fitted just garbage? I copied the output for
model_fit.summary()below. Any sugestions for improvements?
Before I go fiddle with different parameters, I want to make sure that my understanding of the concepts is correct.
I can post more code or an example of my dataset if this helps. Many thanks for your help!
Zero Mean - GARCH Model Results
=================================================================================
Dep. Variable: Returns mean adjusted R-squared: 0.000
Mean Model: Zero Mean Adj. R-squared: 0.000
Vol Model: GARCH Log-Likelihood: -8545.06
Distribution: Normal AIC: 17096.1
Method: Maximum Likelihood BIC: 17115.1
No. Observations: 4110
Date: Thu, Sep 01 2022 Df Residuals: 4110
Time: 11:40:24 Df Model: 0
Volatility Model
===========================================================================
coef std err t P>|t| 95.0% Conf. Int.
---------------------------------------------------------------------------
omega 0.0454 6.394e-02 0.710 0.478 [-7.994e-02, 0.171]
alpha[1] 0.0612 5.064e-02 1.209 0.227 [-3.804e-02, 0.160]
beta[1] 0.9319 6.049e-02 15.406 1.500e-53 [ 0.813, 1.050]
===========================================================================
Covariance estimator: robust
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