# Question: Many auto regressions are mean reverting Mean reverting means that the forecasts

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

ŷt = 50 + 0.8 y t–1

(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 auto regression with positive slope (0 < b1 < 1) predict an increase in the time series? A decrease?

ŷt = 50 + 0.8 y t–1

(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 auto regression with positive slope (0 < b1 < 1) predict an increase in the time series? A decrease?

## Answer to relevant Questions

1. Zip codes are an example of numerical data. 2. Quantitative data consist of numbers along with their units. 3. Cases is another name for the columns in a data table. 4. The number of rows in a data table is indicated by ...A major bank collected data on 100,000 of its customers (income, sex, location, number of cards, etc.) and then computed how much profit it made from the account of these customers during 2010. (a) Identity whether the data ...A chain of photography and electronics stores created a Web site to promote its photography lessons. The number of weekly visitors grew steadily, at a rate of about 300 new visitors each week. This timeplot shows the counts ...This analysis compares the model in the text that has the level of shipments as the response to a model that uses the change in the shipments as the response. (These data are monthly, based on the seasonally adjusted data ...These data measure imports of goods and services into the United States, quarterly from 1981 through 2011 (n = 124 quarters). The data are given in billions of dollars, expressed at an annual rate. The data table includes a ...Post your question