# Are ARIMA coefficients bounded?

I don't have a lot of background in TS analysis and I haven't found references that are clear on this. Hopefully someone here can help me understand this.

I'm optimising ARIMA coefficients for a multiple sets of orders. From my understanding, absolute value of MA coefficients should always be < 1 according due to the bound of invertibility. Then I've seen that same goes for AR coefficients (bound of stationary). Most of the references that I've found derive this with AR(p=1) or MA(q=1) but not for higher order models.

• Would it be safe to set the constraint on all ARMA coefficients that they should be between -0.99 and 0.99.
• Also, what would it mean if after the optimisation, the coefficients were pushed to the boundaries.

Thanks,

• Does this answer your question? Regularization for ARIMA models – Adrian Keister Apr 2 at 22:24
• "absolute value of AR/MA coefficients should always be < 1..." is not correct. – Michael Apr 3 at 14:38