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

[Alexios Ghalanos]

Robust standard errors formula/details are provided in the vignette if I am not mistaken, but will add some additional details (re the calculation and the additional arguments to ugarchfit in the development version) when I find some time.

Alexios

> On 17 Sep 2014, at 15:12, alexios ghalalanos <alexios at 4dscape.com> wrote:
> 
> Gareth,
> 
> 1. For such a small dataset (242 points) try using QML (i.e.
> distribution="norm").
> 2. Also, don't use "coredata" and don't multiply by 100.
> Instead, pass the returns as xts (as is).
> 
> -Alexios
> 
> 
>> On 17/09/2014 12:33, Gareth McEwan wrote:
>> 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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