# Interpretation of AR, MA, ARIMA models

In literature have read, that model: AR=> acf damped exponents and/or damped sine wave. pacf rare outputs beyond the confidence interval. The number of outputs per confidence interval in pacf determines the order p of the AR(p) model.

MA=> pacf damped exponents and/or damped sine wave.acf rare outputs beyond the confidence interval. The number of outputs per confidence interval in acf determines the order q of the MA(q) model.

1. Is it possible for the AR model, the values of the acf to cross the confidence interval or the values must be inside it? Is it possible for MA models, the values of the pacf to cross the confidence interval or the values must be inside it?

2.The figure shows that the acf crosses the interval twice and the pacf once.What model could it be?

3.Is it possible to programmatically determine the damped exponents and the sine wave.What formulas to use to identify them?

4.This question most of all leads me to confusion. For example ARIMA (1,d,0). acf decays exponentially, pacf is only the first nonzero. In my understanding it is AR (1)...

5.In General, I want to programmatically determine which model is currently AR, MA, ARMA or ARIMA. On the Internet, a lot of interpretations of acf, pacf. And in many of them there is no clear logic to define models. What can you advise?

• I specifically divided the questions into numbers. Because someone doesn't know all the answers. – user287629 Feb 26 at 16:27