Autocorrelation Values for Stationary Process

I'm doing a self study out of Box, Jenkins, Reinsal, Ljung - Time Series Analysis Forecasting and Control. Problem 2.2 has me stuck (it seems so simple) it asks:

State whether or not a stationary stochastic process can have the following values of autocorrelations: $$a) \ \rho_1 = .8 \quad \rho_2=0.55\quad \rho_k = 0 \quad k>2$$ $$b) \ \rho_1 = .8 \quad \rho_2 = .28 \quad \rho_k = 0 \quad k>2$$

I'm trying to get some intuition for this. I can't see any reason where there would be restrictions on the autocorrelation function or what values it may take which probably exposes a big hole in my understanding of the chapter. Any advice/intuition/solutions are welcome.

• You need to add the self study tag. – Michael Chernick Nov 20 '17 at 3:57
• Did you read about the roots of the characteristic polynomial? Stationarity for AR processes depend on whether or not the roots of the characteristic polynomial fall inside the unity circle. – Michael Chernick Nov 20 '17 at 4:21
• @MichaelChernick Thanks, I think this points me in the right direction. – mv3 Nov 20 '17 at 13:43