I've been struggling with the following problem for quite a while now, and have been unable to identify a pattern;

You have a geometric series $Y$ for which we have the following rule: $$Y_{t+1} = \beta_0 + \beta_1 Y_t + \beta_2 Y_{t-1}.$$

All beta variables ($\beta_0$, $\beta_1$, and $\beta_2$) are constants, while $Y_t$ and $Y_{t-1}$ are the first and second lags of $Y_{t+1}$. Find an expression for $Y_{t+h}$ as a function of $Y_t$ and $Y_{t-1}$ using finite sigma notation.

If anyone can offer any advise about how I would go about solving it, I would be very grateful.


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