Time series questions in R

Question

Let $X_t$ be the process satisfying the following equation:$$X_t = \phi X_{t−1} + Z_t − \theta Z_{t−2},\,\theta > 0,$$where $Z_t$ is a white noise process.

1. What conditions on $\phi$ and $\theta$ are required for this process to be stationary, causal and invertible? Under what conditions, the model is redundant?

2. Suppose $\phi = 0.65$ and $\theta = 0.32$. Simulate $1000$ data points from the above model and compute the sample ACF and PACF.