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This question asks you to think about an AR(1) model with a negative slope parameter (specifically, -1 < β1 < 0). Suppose that you have time-series data, denoted y1, y2, ... , yn, that follows the AR(1) model with negative slope. For concreteness, let's say that you run the AR(1) regression and obtain an intercept estimate of 15 and a slope estimate of -0.5.
a. What is the sign of the correlation between yt and yt-1?
b. How about the sign of the correlation between yt and yt-2? between yt and yt-3? Do you see a pattern?
c. The formula for the mean of the AR(1) process remains the same. In this case, the estimated mean would be 15/(1-(-0.5)) = 10. Suppose that your last observation yn is equal to 20. Use the OLS estimates in order to provide forecasts (just point estimates, not intervals) for the next five periods yn+1, yn+2, ..., yn+5. Comment on how the forecasts compare to the mean level of the AR(1) process.
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