'GARCHLags' and 'ARCHLags' properties can only be positive vectors. See function syntax. This is because the 'GARCHLags' input corresponds to the lag of the 'GARCH' coefficients as is the case for 'ARCHLags'. Refer to this example:
g = garch('GARCHLags',[1 2 3],'GARCH', [0.06 0.07 0.08], 'ARCHLags',[1 2], 'ARCH', [0.09 0.10])
g =
garch with properties:
Description: "GARCH(3,2) Conditional Variance Model (Gaussian Distribution)"
Distribution: Name = "Gaussian"
P: 3
Q: 2
Constant: NaN
GARCH: {0.06 0.07 0.08} at lags [1 2 3]
ARCH: {0.09 0.1} at lags [1 2]
Offset: 0
You can read more about GARCH models at this link https://www.mathworks.com/help/econ/what-is-a-conditional-variance-model.html#btbsicl This gives a good explanation about the lags and the coefficients.
So why is garch(0,0) valid then?
It's valid because it creates a default GARCH model without any GARCH or ARCH coefficients. Refer example here.
