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.
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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