GARCH estimation using the arch package
python xgarch_gjr_mean.py gives
symbol = sp500
first and last dates:
1993-01-29 24.4525
2025-04-21 516.7299
Constant Mean - GARCH Model Results
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Dep. Variable: SPY R-squared: 0.000
Mean Model: Constant Mean Adj. R-squared: 0.000
Vol Model: GARCH Log-Likelihood: -10782.0
Distribution: Standardized Skew Student's t AIC: 21576.0
Method: Maximum Likelihood BIC: 21618.1
No. Observations: 8111
Date: Mon, Apr 21 2025 Df Residuals: 8110
Time: 11:08:43 Df Model: 1
Mean Model
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coef std err t P>|t| 95.0% Conf. Int.
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mu 0.0601 8.534e-03 7.045 1.858e-12 [4.339e-02,7.684e-02]
Volatility Model
============================================================================
coef std err t P>|t| 95.0% Conf. Int.
----------------------------------------------------------------------------
omega 0.0128 2.557e-03 5.001 5.703e-07 [7.775e-03,1.780e-02]
alpha[1] 0.1125 9.875e-03 11.390 4.673e-30 [9.313e-02, 0.132]
beta[1] 0.8830 9.782e-03 90.268 0.000 [ 0.864, 0.902]
Distribution
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coef std err t P>|t| 95.0% Conf. Int.
---------------------------------------------------------------------------
eta 6.4613 0.459 14.066 6.128e-45 [ 5.561, 7.362]
lambda -0.0955 1.398e-02 -6.831 8.456e-12 [ -0.123,-6.812e-02]
===========================================================================
Covariance estimator: robust
return statistics
series #obs mean sd Sharpe skew kurt min max
raw 8111 0.0327 1.1808 0.4395 -0.0074 11.7703 -10.9543 14.5078
norm 8111 0.0317 1.0026 0.5014 -0.5314 2.1002 -7.9006 4.2413
Volatility-bin statistics:
vol_bin #obs mean sd Sharpe skew kurt min max
0.0-1.0 4851 0.0247 0.7344 0.5349 -0.5599 2.0302 -4.1942 2.9320
1.0-2.0 2838 0.0331 1.3385 0.3925 -0.3243 1.8351 -7.2593 5.7957
>=2.0 422 0.1213 2.9225 0.6591 0.2165 2.8707 -10.9543 14.5078