Testing For ARCH

1
Testing For ARCH

• Step 1 Estimate the yt sequence using the
  "best fitting" ARMA model (or regression model)
  and obtain the squares of the fitted errors .
  Consider the regression equation
• If there are no ARCH effects a1 a2 0

2
Technical Issues

• All the coefficients should be statistically
  significant
• No simple way to distinguish between various ARCH
  and GARCH models
• Since the variance cannot be negative, all
  coefficients should be POSITIVE.

3
GARCH.SRC
GARCH will estimate (via MLE) a number of
ARCH-type models, with up to an ARMA(13,13) for
the conditional mean equation, up twenty-five
exogenous variables, and up to an xARCH(4,4) for
the conditional variance with up to thirteen
exogenous/user-input variables in the conditional
variance. Syntax _at_GARCH(options)
series start end nresids cvar
ltsuppl. cardgt (OPTIONAL exogenous series for
the mean equation w/
EXOG option) ltsuppl. cardgt (OPTIONAL
exogenous series for the
variance equation w/ VEXOG) Also,
this version includes non-negativity
constraints. Parameters depvar is
the series for the dependant variable start
end are the start and end points for the
depvar nresids is the series to which
the normalized residuals are saved cvar
is the series to which the estimated
conditional variance is saved.
4
GARCH.SRC OPTIONS
DET NONE/CONSTANT The deterministic
components for the mean. AR 0
Number of autoregressive terms in mean, 0 to 13
MA 0 Number of moving average
terms in mean, 0 to 13 P 0
Number lagged variance terms in conditional
variance, 0 to 4 Q
1 Number of lagged squared residuals in
conditional variance, 0 or 1 to
4 EXOG/NOEXOG Use EXOG to alert the proc
of an additional suppl.
card for exogenous variables additively
entering the mean equation.
UP TO TWENTY-FIVE EXOGENOUS
VARIABLES CAN BE USED VEXOG/NOVEXOG Use
VEXOG to alert the proc of an additional suppl.
card for exogenous variables
additively entering the
conditional variance equation. UP TO
THIRTEEN EXOGENOUS VARIABLES CAN BE
USED AIM/NOAIM Add an ARCH-IN-MEAN
term a function of the conditional
variance term enters the mean equation
5
GARCH.SRC OPTIONS FOR MODELS
MOD ARCH/GARCH/IGARCH/EGARCH/LGARC
H/LIGARCH The type of ARCH
model to be estimated The
ARCH(q) model has q lagged squared
residuals in the conditional variance
The GARCH(p,q) model adds p lagged
conditional variance terms to
the ARCH(p) The IGARCH(p,q)
model forces the coefficients
in the conditional variance to sum to one
The EGARCH(p,q) is the exponential
GARCH model of Nelson
(1991) The LGARCH(p,q) adds a
leverage term to account
for asymmetry/skewness to a GARCH(p,q) model
The LIGARCH(p,q) is the LGARCH model
with the IGARCH constraint