[R-SIG-Finance] rugarch and fGarch
Belgarath
marco.cora at googlemail.com
Wed Jun 13 15:13:16 CEST 2012
Hello Alexios,
thank you for the quick reply! Apologies but yesterday yahoo finance was not
working so could not follow up with an appropriate reproducible example:
1)
----
getSymbols("^GSPC", src="yahoo")
SPY.log.ret=ClCl(GSPC)
GA3=garchFit(formula=~arma(1,0)+aparch(1,1),data=last(SPY.log.ret,1371),cond.dist="sstd")
summary(GA3)
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=last(SPY.log.ret,1371))
show(GAA3)
volforecast=ugarchroll(spec=modeltofit,data=last(SPY.log.ret,1371), n.ahead
= 21,
forecast.length = 420, refit.every = 21)
sigma=as.data.frame(volforecast,which="density",n.ahead=21)
sigmat <- as.POSIXct(strptime(sigma[,1],format="%Y-%m-%d"))
sigma2 <- xts(sigma[,3],order.by=sigmat)*100*sqrt(252)
plot(sigma2)
---
Detailed results are below, but to reply to your points:
2) rugarch omega is 0.000618 t:1.5062e+00 p:0.132023 while fGarch omega
is 3.922e-04 t:3.970 p:7.19e-05 which is more significant.
3) Is the code above usage correct to extract the forecasts? I tried to use
the sigma=as.data.frame(volforecast, which = "sigma") but it only return the
first 21 forecasts. How do I extract the long term mean of the st dev?
4) I have one more question: the dates in the
sigma=as.data.frame(volforecast,which="density",n.ahead=21) are alligned
with the date the forecast refers to no the date the forcast is made (ie. it
will be delayed by 21 days in a chart) correct?
Thank you again for the help and the package!
Marco
*****************
> 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 0.000197 0.000007 2.7154e+01 0.000000
ar1 -0.086149 0.000122 -7.0664e+02 0.000000
omega 0.000618 0.000411 1.5062e+00 0.132023
alpha1 0.090424 0.010405 8.6908e+00 0.000000
beta1 0.916128 0.010687 8.5724e+01 0.000000
gamma1 1.000000 0.000000 2.5738e+06 0.000000
delta 0.844145 0.130924 6.4476e+00 0.000000
skew 0.833679 0.028852 2.8895e+01 0.000000
shape 7.325115 1.542399 4.7492e+00 0.000002
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000197 NaN NaN NaN
ar1 -0.086149 NaN NaN NaN
omega 0.000618 NaN NaN NaN
alpha1 0.090424 NaN NaN NaN
beta1 0.916128 NaN NaN NaN
gamma1 1.000000 NaN NaN NaN
delta 0.844145 NaN NaN NaN
skew 0.833679 NaN NaN NaN
shape 7.325115 NaN NaN NaN
LogLikelihood : 4133.434
Information Criteria
------------------------------------
Akaike -6.0167
Bayes -5.9824
Shibata -6.0168
Hannan-Quinn -6.0038
Q-Statistics on Standardized Residuals
------------------------------------
statistic p-value
Lag10 11.45 0.2459
Lag15 16.60 0.2780
Lag20 18.74 0.4737
H0 : No serial correlation
Q-Statistics on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag10 29.72 0.0004892
Lag15 33.15 0.0027369
Lag20 36.37 0.0094979
ARCH LM Tests
------------------------------------
Statistic DoF P-Value
ARCH Lag[2] 15.81 2 0.0003695
ARCH Lag[5] 16.98 5 0.0045286
ARCH Lag[10] 30.99 10 0.0005890
Nyblom stability test
------------------------------------
Joint Statistic: NA
Individual Statistics:
mu 0.2380
ar1 0.2163
omega 0.1923
alpha1 0.1939
beta1 0.2190
gamma1 NA
delta 0.2084
skew 0.1054
shape 0.2543
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 0.3575 0.720737
Negative Sign Bias 2.5732 0.010180 **
Positive Sign Bias 2.7813 0.005489 ***
Joint Effect 14.4861 0.002313 ***
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 30.47 0.046075
2 30 40.31 0.078949
3 40 54.67 0.049050
4 50 74.99 0.009861
Elapsed time : 5.466
> summary(GA3)
Title:
GARCH Modelling
Call:
garchFit(formula = ~arma(1, 0) + aparch(1, 1), data = last(SPY.log.ret,
1371), cond.dist = "sstd")
Mean and Variance Equation:
data ~ arma(1, 0) + aparch(1, 1)
<environment: 0x000000000e8e8e68>
[data = last(SPY.log.ret, 1371)]
Conditional Distribution:
sstd
Coefficient(s):
mu ar1 omega alpha1 gamma1 beta1
0.00022015 -0.08726888 0.00039220 0.09300673 0.99999999 0.90917036
delta skew shape
0.95108469 0.83598044 7.13436954
Std. Errors:
based on Hessian
Error Analysis:
Estimate Std. Error t value Pr(>|t|)
mu 2.202e-04 2.702e-04 0.815 0.415301
ar1 -8.727e-02 2.557e-02 -3.413 0.000643 ***
omega 3.922e-04 9.879e-05 3.970 7.19e-05 ***
alpha1 9.301e-02 1.157e-02 8.035 8.88e-16 ***
gamma1 1.000e+00 1.085e-02 92.183 < 2e-16 ***
beta1 9.092e-01 1.112e-02 81.759 < 2e-16 ***
delta 9.511e-01 1.667e-01 5.705 1.16e-08 ***
skew 8.360e-01 3.064e-02 27.284 < 2e-16 ***
shape 7.134e+00 1.543e+00 4.625 3.75e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Log Likelihood:
4131.182 normalized: 3.013262
Description:
Wed Jun 13 14:57:49 2012 by user: cora
Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test R Chi^2 1584.761 0
Shapiro-Wilk Test R W 0.9597795 0
Ljung-Box Test R Q(10) 12.32339 0.2639963
Ljung-Box Test R Q(15) 16.8469 0.3280988
Ljung-Box Test R Q(20) 18.48151 0.5557211
Ljung-Box Test R^2 Q(10) 9.478356 0.4873852
Ljung-Box Test R^2 Q(15) 12.33782 0.6532996
Ljung-Box Test R^2 Q(20) 13.34997 0.8618686
LM Arch Test R TR^2 29.52316 0.003292551
Information Criterion Statistics:
AIC BIC SIC HQIC
-6.013395 -5.979106 -6.013480 -6.000563
--
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