arima estimate error with garch

I am attempting to estimate an arima model using the following data and code and I receive an error that I cannot explain. It says that Q cannot be zero, but it isn't. I have set Q to 1 in the model parameters.

Vacancy = [0.00560410649477194;0.00524853168475042;0.00238308339410447;0.00853974938881424;0.00908073791573352;0.00691790589264439;0.00303000179373218;0.00234702676185684;0.00308768370467530;0.000404948868887228;0.00151098376431826;-0.000719726188241399;0.00358057285276520;-0.000903514492771818;0.000486432830662964;-0.00281521882134218;-0.00194152296552609;-0.000720527452380812;0.000878011283635613;-0.00394684134056665;-0.00164891229969798;-0.00184849694448057;-0.00204229556740551;-0.00174202975109919;-0.000471920351107463;-0.00138653335938199];

N = length(Vacancy);
model = arima('ARLags',1,'Variance',garch(1,1));
fit = estimate(model,Vacancy);

Warning: Lower bound constraints are active; standard errors may be inaccurate.
> In arima.estimate at 1094
Estimated variance model is invalid.

Caused by:
    Error using garch/validateModel (line 782)
    Non-zero degree P requires a non-zero degree Q.

Answer 1

[Roger Wohlwend]

The error message is a bit misleading. You did specify Q = 1. I have no idea why the error occurs but I have also received it in the past. My explanation for the error is that it is apparently not always possible to estimate a valid model. GARCH models can be tricky. They are not like ARMA models where you can choose R and M however you like it and you always get a valid model. So, if Matlab is not capable of estimating a model, then all you can do is changing the specification. In your case choose a garch(0,1) model and everything will be allright.

Answer 2

[Karl-Martin]

Allthough you did specify Q=1, the parameter can be excluded from the model.

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 if the Q parameter is too close to zero it is excluded and you end up with an invalid GARCH(1,0) model which leads to the error.