rugarch and fGarch
1. Please examples with reproducible data for such a detailed question. SPX.log.ret is not a commom data object found in any of the packages I know of. 2. How is the significance much lower? Looking at the Pr(>|t|) column they both look very significant across all parameters. The fact that the robust s.e. have NaN means that the robust hessian could not be calculated indicating that you need to tune the solver/use scaling (set 'fit.control=list(scale=1)'). Looking at the results, this is likely because of the 'gamma' parameter hitting its upper limit. 3. This is a rolling out of sample forecast which means that you are getting rolling estimates using 100 out of sample data points from the end of your dataset. As to the "expected" vol in 21 days ROLLING 1 day at a time, 'n.ahead=21', you need to pass this argument to the as.data.frame method or better still use: 'sigma=as.data.frame(volforecast, which = "sigma")'. This will be reverting to its long run mean. I really don't know what you expect as being reasonable or not. -Alexios
On 12/06/2012 08:49, Belgarath wrote:
Dear All,
first of all thanks for the great package!
I'm trying to get volatility forecasts. So I tried a couple of packages and
I really like the roll functionality provided within the rugarch package but
am finding inconsistencies with the results from two garch packages:
1)
I run
GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=SPX.log.ret,cond.dist="sstd")
modeltofit=ugarchspec(variance.model = list(model = "apARCH", garchOrder =
c(1, 1),
submodel = NULL, external.regressors = NULL, variance.targeting = FALSE),
mean.model = list(armaOrder = c(1, 0), include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE),
distribution.model = "sstd", start.pars = list(), fixed.pars = list())
GAA3=ugarchfit(spec=modeltofit,data=SPX.log.ret)
As you can see from the results below the parameter coefficients are
different but similar but the significance is much lower for rugarch. Do you
know why?
2)
I then run
volforecast=ugarchroll(spec=modeltofit, data = last(SPX.log.ret,550),
n.ahead = 42,
forecast.length = 100, refit.every = 25)
sigma=as.data.frame(volforecast)
sigmat<- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
sigma2<- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
And the results seems to me too low to represent the expected vol in 21
days. Could you please point me in the right direction?
Thank you!
**********************
RESULTS
**********************
fGarch----------------------
summary(GA3)
Title:
GARCH Modelling
Call:
garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = SPX.log.ret,
cond.dist = "sstd")
Mean and Variance Equation:
data ~ arma(1, 0) + aparch(1, 1)
<environment: 0x000000000c09f038>
[data = SPX.log.ret]
Conditional Distribution:
sstd
Coefficient(s):
mu ar1 omega alpha1 gamma1 beta1
0.00025599 -0.06942414 0.00011829 0.08504516 0.99999999 0.91557956
delta skew shape
1.11700143 0.86337982 5.35586013
Std. Errors:
based on Hessian
Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu 2.560e-04 2.023e-04 1.266 0.205659
ar1 -6.942e-02 2.332e-02 -2.977 0.002907 **
omega 1.183e-04 3.481e-05 3.399 0.000677 ***
alpha1 8.505e-02 1.285e-02 6.616 3.69e-11 ***
gamma1 1.000e+00 1.441e-02 69.414< 2e-16 ***
beta1 9.156e-01 1.006e-02 91.041< 2e-16 ***
delta 1.117e+00 1.962e-01 5.693 1.25e-08 ***
skew 8.634e-01 2.755e-02 31.337< 2e-16 ***
shape 5.356e+00 8.347e-01 6.416 1.40e-10 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Log Likelihood:
5271.315 normalized: 3.1433
Description:
Tue Jun 12 09:02:05 2012 by user: cora
Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test R Chi^2 2459.58 0
Shapiro-Wilk Test R W 0.9528365 0
Ljung-Box Test R Q(10) 11.72432 0.3039307
Ljung-Box Test R Q(15) 15.45374 0.4192542
Ljung-Box Test R Q(20) 21.50983 0.3676896
Ljung-Box Test R^2 Q(10) 90.12559 5.107026e-15
Ljung-Box Test R^2 Q(15) 91.15075 6.047385e-13
Ljung-Box Test R^2 Q(20) 91.74618 3.664247e-11
LM Arch Test R TR^2 26.18211 0.01011463
Information Criterion Statistics:
AIC BIC SIC HQIC
-6.275867 -6.246754 -6.275924 -6.265082
******************************+
******************************
rugarch--------------------
show(GAA3)
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : apARCH(1,1)
Mean Model : ARFIMA(1,0,0)
Distribution : sstd
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.000237 0.000190 1.2474e+00 0.212265
ar1 -0.069601 0.024100 -2.8881e+00 0.003876
omega 0.000175 0.000148 1.1823e+00 0.237092
alpha1 0.084114 0.011113 7.5687e+00 0.000000
beta1 0.920963 0.009835 9.3640e+01 0.000000
gamma1 1.000000 0.000000 2.6926e+06 0.000000
delta 1.025983 0.159330 6.4393e+00 0.000000
skew 0.860581 0.027580 3.1203e+01 0.000000
shape 5.561683 0.875725 6.3509e+00 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000237 NaN NaN NaN
ar1 -0.069601 NaN NaN NaN
omega 0.000175 NaN NaN NaN
alpha1 0.084114 NaN NaN NaN
beta1 0.920963 NaN NaN NaN
gamma1 1.000000 NaN NaN NaN
delta 1.025983 NaN NaN NaN
skew 0.860581 NaN NaN NaN
shape 5.561683 NaN NaN NaN
LogLikelihood : 5291.85
Information Criteria
------------------------------------
Akaike -6.3004
Bayes -6.2712
Shibata -6.3004
Hannan-Quinn -6.2896
Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 8.594 0.4756
Lag15 13.965 0.4523
Lag20 20.967 0.3386
H0 : No serial correlation
Q-Statistics on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag10 28.13 0.0009072
Lag15 31.84 0.0042245
Lag20 35.40 0.0124798
ARCH LM Tests
------------------------------------
Statistic DoF P-Value
ARCH Lag[2] 12.84 2 0.001630
ARCH Lag[5] 14.26 5 0.014050
ARCH Lag[10] 28.19 10 0.001683
Nyblom stability test
------------------------------------
Joint Statistic: NA
Individual Statistics:
mu 0.90793
ar1 0.11145
omega 0.91076
alpha1 0.53714
beta1 0.60241
gamma1 NA
delta 0.84958
skew 0.06079
shape 0.50963
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 2.1 2.32 2.82
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.7081 0.478964
Negative Sign Bias 2.7958 0.005236 ***
Positive Sign Bias 2.7352 0.006301 ***
Joint Effect 15.8663 0.001208 ***
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 53.65 3.733e-05
2 30 62.55 2.942e-04
3 40 67.52 3.081e-03
4 50 86.60 7.431e-04
Elapsed time : 4.712
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