Estimate GARCH(4,1) using estimate: Parameter GARCH{2} is missing

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Hi,
I want to fit an AR(1) Model to a time series of returns (x) and the variance process follows a GARCH(4,1) model.
model = arima('ARLags',1,'Variance',garch(4,1))
fit = estimate(model,x)
returns:
ARIMA(1,0,0) Model:
--------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Constant -0.000754276 0.000531875 -1.41815
AR{1} 0.223266 0.0279149 7.99808
GARCH(4,1) Conditional Variance Model:
----------------------------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Constant 1.77228e-05 3.59061e-06 4.93587
GARCH{1} 0.55604 0.113503 4.89891
GARCH{3} 0.193253 0.193158 1.00049
GARCH{4} 0.065569 0.0953147 0.687922
ARCH{1} 0.176294 0.0259334 6.79798
Why is the parameter GARCH{2} missing in the table? Is it because it may be very unsignificant? I mean the parameters GARCH{3} and GARCH{4} are pretty unsignificant as well. Or are there too few observations? The time series x is 1545 observations long. When I limit the estimation to a fit period of just 1000 observations via
model = arima('ARLags',1,'Variance',garch(4,1))
fit = estimate(model,x(1:1000))
it returns:
ARIMA(1,0,0) Model:
--------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Constant 0.000184079 0.000783618 0.234909
AR{1} 0.234824 0.0336974 6.9686
GARCH(1,1) Conditional Variance Model:
----------------------------------------
Conditional Probability Distribution: Gaussian
Standard t
Parameter Value Error Statistic
----------- ----------- ------------ -----------
Constant 4.899e-05 1.53734e-05 3.18668
GARCH{1} 0.796332 0.279077 2.85345
ARCH{1} 0.157239 0.0455136 3.45478
Now the result is a GARCH(1,1) model, allthough I defined the model to be a GARCH(4,1).
Using Econometrics Toolbox for MATLAB R2014a.
Thanks in Advance!

Accepted Answer

Karl-Martin
Karl-Martin on 10 Jan 2015
Nevermind, I found the solution. In the 'garch.m' function of the Econometrics toolbox it is stated:
% o The coefficients GARCH and ARCH are each associated with an
% underlying lag operator polynomial and subject to a near-zero
% tolerance exclusion test. That is, each coefficient is compared to
% the default zero tolerance 1e-12, and is included in the model only
% if the magnitude is greater than 1e-12; if the coefficient magnitude
% is less than or equal to 1e-12, then it is sufficiently close to zero
% and excluded from the model. See LagOp for additional details.
So the parameters are too close to zero and therefore excluded from the model...

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