Many auto regressions are mean-reverting. Mean reverting means that the forecasts eventually tend back to (revert to) the mean of the time series. For example, a manager uses an AR(1) model to predict...

Many auto regressions are mean-reverting. Mean reverting means that the forecasts eventually tend back to (revert to) the mean of the time series. For example, a manager uses an AR(1) model to predict sales next week using sales in recent weeks. Sales typically run about
250,000 per week. The estimating equation (with sales in thousands of dollars) is

(a) If sales this week are
250,000 (the mean level), what does the equation forecast for next week?

(b) If sales this week are
300,000 (50,000 above the mean), does the equation forecast sales to increase farther above the mean or to return toward the mean?

(c) In general, when does a first-order autoregression with positive slope
 predict an increase in the time series? A decrease?