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library(rugarch)
data(sp500ret)
spec = ugarchspec(variance.model = list(model = "eGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(1, 1), arfima = FALSE), distribution.model = "std")
fit = ugarchfit(spec = spec, data = sp500ret, out.sample = 0, solver = "solnp", solver.control = list(trace = 0))
fit
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : eGARCH(1,1)
Mean Model : ARFIMA(1,0,1)
Distribution : std
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.000437 0.000092 4.7658 2e-06
ar1 0.731213 0.074840 9.7703 0e+00
ma1 -0.760652 0.071457 -10.6449 0e+00
omega -0.113595 0.019917 -5.7033 0e+00
alpha1 -0.078280 0.009018 -8.6808 0e+00
beta1 0.988013 0.002127 464.4841 0e+00
gamma1 0.110265 0.010801 10.2092 0e+00
shape 6.521778 0.554433 11.7630 0e+00
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000437 0.000089 4.8897 1e-06
ar1 0.731213 0.040019 18.2716 0e+00
ma1 -0.760652 0.039183 -19.4127 0e+00
omega -0.113595 0.021342 -5.3225 0e+00
alpha1 -0.078280 0.011251 -6.9577 0e+00
beta1 0.988013 0.002277 433.9338 0e+00
gamma1 0.110265 0.011002 10.0220 0e+00
shape 6.521778 0.675463 9.6553 0e+00
LogLikelihood : 18161.66
Information Criteria
------------------------------------
Akaike -6.5738
Bayes -6.5643
Shibata -6.5738
Hannan-Quinn -6.5705
Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 14.92 0.06067
Lag15 26.67 0.01380
Lag20 32.01 0.02190
H0 : No serial correlation
Q-Statistics on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag10 4.369 0.8224
Lag15 6.145 0.9407
Lag20 7.974 0.9790
ARCH LM Tests
------------------------------------
Statistic DoF P-Value
ARCH Lag[2] 1.647 2 0.4389
ARCH Lag[5] 1.894 5 0.8636
ARCH Lag[10] 4.275 10 0.9341
Nyblom stability test
------------------------------------
Joint Statistic: 5.9612
Individual Statistics:
mu 0.2473
ar1 1.1236
ma1 1.0484
omega 0.2594
alpha1 2.5779
beta1 0.2392
gamma1 0.1184
shape 1.7424
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.89 2.11 2.59
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.1619 0.8714217
Negative Sign Bias 2.7171 0.0066062 ***
Positive Sign Bias 1.8662 0.0620719 *
Joint Effect 19.7580 0.0001905 ***
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 49.77 0.0001416
2 30 60.89 0.0004774
3 40 75.52 0.0004057
4 50 81.64 0.0023565
Elapsed time : 3.416406
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