Suggest a model from ACF and PACF values

Question

Considera sample of 50 observations from a stationary process with

$$\begin{array}{c|c|c|} \text{lag} & \text{acf} & \text{pacf} \\ \hline 1 & 0.9 & 0.9 \\ \hline 2& 0.85 & 0.4\\ \hline 3&0.7&0.1\\ \hline \end{array}$$

How do I suggest an appropriate model using the above information.

From my understanding, significance of ACF and PACF values were checked using:$ H_{0}: \rho=0$ rejected at 5% level of significance if $|\rho| >\frac{1.96}{\sqrt(50)}$. I found that only the last value of pacf is non significant.

(1)Can I say that the model is ARMA(2,3)? (2) how to decide if it is AR, MA or ARMA?

NB: this was a question asked in an examination. To be worked out manually.

Answer 1

THE BIG PRINT:

Since the ACF is dominant i.e.has the most significant values the process is autoregressive (AR) . The order of the AR model is determined by the # of significant values in the subordinate structure ... in this case the PACF .. thus 2.

The answer is (2,0,0)

THE LITTLE PRINT:

When does this simple strategy work ...

1) When there are no step/level shifts in the data

2) When there are no deterministic trends in the data

3) When there are no pulses in the data

4) When there are no seasonal pulses in the data

5) when the suggested model has constant parameters and constant error variance over time