ARMA estimation with ARMAX function

To whom it may concern,

I have to produce some macroeconomic forecastings by means of an ARMA model. So, I am using the function armax to estimate my model. I have seen that, in order to estimate an ARMA(2,1) model, I need 8 observations at least. Since I need to estimate my free parameters (3) and the covariance matrix (which has 6 non-repeating entries), shouldn't it need at least 9 observations? More in general, which is the minimum number of observations needed to estimate an ARMA(p,q) model by means of armax function? Many thanks for you your attention! Best,

Fabio.