AR(1) Process - Time Series

Question

Is the time series $X_t = Y_t - 0.8Y_{t-1}$ an AR(1) process if $Y_t$ is a white noise process?

I am guessing that the answer is yes since the time series $X_t$ depends upon $Y_{t-1}$, i.e. only the first lag. Is this conclusion correct?

Answer 1

In general an AR($p$) process can be written as

$$ x_t = c + \sum_{k=1}^p \phi_k x_{t-k} + \eta_k $$

where $\eta_k$ is white noise, and $\phi_1, \cdots, \phi_k$ and $c$ are constants. So no, your process is not an AR($p=1$) process.