[R-SIG-Finance] Estimating the T-S Garch model

Thu May 1 23:23:47 CEST 2008

I am trying to estimate a T-S Garch model with the following code -

library(fGarch)
myFinCenter =  "GMT"
dframe=read.csv(file="loss.csv")
dframe[1:5,]
loss=as.timeSeries(dframe)
head(loss)
tail(loss)
fit = garchFit(formula = ~ aparch(1,1), data=loss at Data, delta=1.0,
include.delta=FALSE,trace=FALSE)
summary(fit)
fit2 = garchFit(formula = ~ aparch(1,1), data=loss at Data, delta=1.0,
include.delta=FALSE,leverage=FALSE)

Output is at the end of the email.  I can estimate a model with
nonzero leverage (gamma1 non-zero) but I have problems when I try to
force gamma1 to be zero.  (See message at end of output.  Is there a
problem or have I not understood something.
I am using Windows XP,  R 2.7.0 and fGarch 260.72.  The data-set
loss.csv is attached.

-- 
John C Frain
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.htm
mailto:frainj at tcd.ie
mailto:frainj at gmail.com

############## OUTPUT ##############################

> library(fGarch)
> myFinCenter =  "GMT"
> dframe=read.csv(file="loss.csv")
> dframe[1:5,]
           X       loss
1 1988-01-05 -3.2854337
2 1988-01-06 -2.6706190
3 1988-01-07  0.3662351
4 1988-01-08 -1.8030495
5 1988-01-11  1.1893279
> loss=as.timeSeries(dframe)
> head(loss)
                 TS.1
1988-01-05 -3.2854337
1988-01-06 -2.6706190
1988-01-07  0.3662351
1988-01-08 -1.8030495
1988-01-11  1.1893279
1988-01-12 -0.1981119
> tail(loss)
                 TS.1
2008-01-24 -4.8668943
2008-01-25  0.7808780
2008-01-28  1.7767990
2008-01-29 -1.1739951
2008-01-30 -0.5321964
2008-01-31  1.3622478
> fit = garchFit(formula = ~ aparch(1,1), data=loss at Data, delta=1.0, include.delta=FALSE,trace=FALSE)
> summary(fit)

Title:
 GARCH Modelling

Call:
 garchFit(formula = ~aparch(1, 1), data = loss at Data, delta = 1,
    include.delta = FALSE, trace = FALSE)

Mean and Variance Equation:
 ~arma(0, 0) + ~aparch(1, 1)

Conditional Distribution:
 dnorm

Coefficient(s):
        mu       omega      alpha1      gamma1       beta1
-0.0624601   0.0274496   0.0816745  -0.3396468   0.9100114

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)
mu     -0.062460    0.011934   -5.234 1.66e-07 ***
omega   0.027450    0.005269    5.210 1.89e-07 ***
alpha1  0.081675    0.009555    8.548  < 2e-16 ***
gamma1 -0.339647    0.047851   -7.098 1.27e-12 ***
beta1   0.910011    0.011797   77.139  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Log Likelihood:
 6630.546    normalized:  1.316368

Standadized Residuals Tests:
                                Statistic p-Value
 Jarque-Bera Test   R    Chi^2  5720.432  0
 Shapiro-Wilk Test  R    W      NA        NA
 Ljung-Box Test     R    Q(10)  102.3393  0
 Ljung-Box Test     R    Q(15)  108.0036  4.440892e-16
 Ljung-Box Test     R    Q(20)  118.3874  5.551115e-16
 Ljung-Box Test     R^2  Q(10)  80.30754  4.369838e-13
 Ljung-Box Test     R^2  Q(15)  86.34728  4.738099e-12
 Ljung-Box Test     R^2  Q(20)  88.63123  1.28495e-10
 LM Arch Test       R    TR^2   66.55288  1.405827e-09

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC
-2.630751 -2.624274 -2.630753 -2.628482

Description:
 Thu May 01 20:58:17 2008 by user: John C Frain

> fit = garchFit(formula = ~ aparch(1,1), data=loss at Data, delta=1.0, include.delta=FALSE,leverage=FALSE)

Series Initialization:
 ARMA model:                arma
 Formula mean:              ~ arma(0, 0)
 GARCH model:               aparch
 Formula var:               ~ aparch(1, 1)
 ARMA Order:                0 0
 Max ARMA Order:            0
 GARCH Order:               1 1
 Max GARCH Order:           1
 Maximum Order:             1
 h.start:                   2
 llh.start:                 1
 Length of Series:          5037
 Recursion Init:            mci
 Series Scale:              1.000351

Parameter Initialization:
 Initial Parameters:          $params
 Limits of Transformations:   $U, $V
 Which Parameters are Fixed?  $includes
 Parameter Matrix:
                       U           V      params includes
    mu     -4.830854e-01   0.4830854 -0.04830854     TRUE
    omega   1.000703e-06 100.0703024  0.10007030     TRUE
    alpha1  1.000000e-08   1.0000000  0.10000000     TRUE
    gamma1 -1.000000e+00   1.0000000  0.10000000    FALSE
    beta1   1.000000e-08   1.0000000  0.80000000     TRUE
    delta   0.000000e+00   2.0000000  1.00000000    FALSE
    skew    1.000000e-01  10.0000000  1.00000000    FALSE
    shape   1.000000e+00  20.0000000  4.00000000    FALSE
 Index List of Parameters to be Optimized:
    mu  omega alpha1  beta1
     1      2      3      5
 Persistence:                  0.8797885

Iteration Path:

Now NLMINB

Error in gamma[i] : object is not subsettable
>
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