[R-SIG-Finance] Unusually large t-values from ugarchfit

[Gareth McEwan]

Hi Alexios

I seem to be getting exceptionally big t-values in a lot of my fitting
output (across a number of financial variables). The majority of the
variables are in "monthly log return" format calculated from "monthly price
observations" over the last 20 years (of the 18 log return series 1 is
first-differenced and another is second-differenced). Sample sizes are
small, unfortunately, only around 242 log return observations per variable.

I'm a big fan of reproducible research, but I'm not sure how to get the
data to you. I've attached a .csv document to this email though. If others
are interested, I've selected the FSPI variable (S&P 500 Index) for which
data is easily obtainable. My data is from a local data vendor here in
South Africa. So, this variable is in monthly log returns, multiplied by
100 to put it in percentage form.

# 5: S&P 500 Index (Developed Equity Markets)
# 5: ARMA(2,3)-GARCH(1,1) errors~jsu
spec.FSPI <-
ugarchspec(variance.model=list(model="sGARCH",garchOrder=c(1,1),

 submodel=NULL,external.regressors=NULL,variance.targeting=F),

 mean.model=list(armaOrder=c(2,3),include.mean=T,external.regressors=NULL),
                   distribution.model="jsu")
garch.FSPI <-
ugarchfit(spec=spec.FSPI,data=coredata(FSPI.log.ret),solver="hybrid")
show(garch.FSPI)

Optimal Parameters
------------------------------------
               Estimate      Std. Error      t value       Pr(>|t|)
mu          0.70104    0.000762       919.8719     0.000000
ar1         -1.93142    0.000391    -4944.8270     0.000000
ar2         -0.93236    0.000206    -4534.2598     0.000000
ma1        1.85979    0.000165    11287.6463     0.000000
ma2        0.72827    0.000149      4887.0466     0.000000
ma3       -0.13019    0.000058     -2232.2089     0.000000
omega    1.28003    0.599599            2.1348     0.032776
alpha1    0.21330    0.038001            5.6129     0.000000
beta1      0.74371    0.035146          21.1605     0.000000
skew      -2.35018    1.132755           -2.0747     0.038010
shape      2.19635    0.714951            3.0720     0.002126

Robust Standard Errors:
             Estimate      Std. Error        t value        Pr(>|t|)
mu        0.70104      0.029683        23.61746    0.00000
ar1       -1.93142      0.030470      -63.38848    0.00000
ar2       -0.93236      0.012092      -77.10479    0.00000
ma1       1.85979      0.001194   1558.23243    0.00000
ma2       0.72827      0.000222   3283.16473    0.00000
ma3      -0.13019      0.003171      -41.05573    0.00000
omega    1.28003     4.319409         0.29634    0.76697
alpha1    0.21330     1.281223         0.16648    0.86778
beta1      0.74371     1.042388         0.71347    0.47556
skew      -2.35018     4.813643       -0.48823    0.62538
shape      2.19635     3.490002        0.62933    0.52914

The excessively large t-values are worrying me. Have you found this to be
normal? Or is there something I'm missing in the modelling methodology?

Also, a word on how the Robust Standard Errors are calculated would be
highly appreciated. I find some of the fitted variables have statistically
significant variables in the "Optimal Parameters" output, but which then
become insignificant in the "Robust Standard Errors" output (as in the case
above). Can you provide any guidance on this finding?

Many many thanks for the help !!
Gareth
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