Suppose yao + a₁yt-1 + ut, and u₁ = put-1 + et and et is serially uncorrelated with es where st. (a) Show that the contemporaneous exogeneity assumption does not hold (b) Show that the problem in (a) is solved when yt-2 is included in the model
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- The forecasting staff for the Prizer Corporation has developed a model to predict sales of its air-cushioned-ride snowmobiles. The model specifies that sales S vary jointly with disposable personal income Y and the population between ages 15 and 40, Z, and inversely with the price of the snowmobiles P. Based on past data, the best estimate of this relationship is S=kYZP where k has been estimated (with past data) to equal 100. If Y=11,000,Z=1,200, and P=20,000, what value would you predict for S? What happens if P is reduced to $17,500? How would you go about developing a value for k? What are the potential weaknesses of this model?Plot the logarithm of arrivals for each transportation mode against time, all on the same graph. Which now appears to be growing the fastest?Metropolitan Hospital has estimated its average monthly bed needs as N=1,000+9X where X=timeperiod(months);January2002=0 N=monthlybedneeds Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly seasonal adjustment factors have been estimated, using data from the past five years: Forecast Metropolitans bed demand for January, April, July, November, and December 2007. If the following actual and forecast values for June bed demands have been recorded, what seasonal adjustment factor would you recommend be used in making future June forecasts?
- The Questor Corporation has experienced the following sales pattern over a 10-year period: Compute the equation of a trend line (similar to Equation 5.4) for these sales data to forecast sales for the next year. (Let 2004=0,2005=1, etc., for the time variable.) What does this equation forecast for sales in the year 2014? Use a first-order exponential smoothing model with a w of 0.9 to forecast sales for the year 2014.Logarithms are especially useful for comparing series with two divergent scales since 10 percent growth always looks the same, regardless of the starting level. When absolute levels matter, the raw data are more appropriate, but when growth rates are whats important, log scales are better.Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?
- Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during the fall and winter quarters. The company developed the following quarterly sales forecasting model: Y t=8.25+0.125t2.75D1t+3.50D3t where Y t=predictedsales(million)inquartert 8.25=quarterlysales(million)whent=0 t=timeperiod(quarter)wherethefourthquarterof2002=0,firstquarterof2003=1,secondquarterof2003=2,... D1t={1forfirst-quarterobservations0otherwiseD2t={1forsecond-quarterobservations0otherwiseD3t={1forthird-quarterobservations0otherwise Forecast Savings-Marts sales of patio and lawn furniture for each quarter of 2010.Bell Greenhouses has estimated its monthly demand for potting soil to be the following: N=400+4X where N=monthlydemandforbagsofpottingsoil X=timeperiodsinmonths(March2006=0) Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: Forecast Bell Greenhouses demand for potting soil in March, June, August, and December 2007. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast.A firm experienced the demand shown in the following table. *Unkown future value to be forecast Fill in the table by preparing forecasts based on a five-year moving average, a three-year moving average, and exponential smoothing (with a w=0.9 and a w=0.3). Note The exponential smoothing forecasts may be begun by assuming Y t+1=Yt. Using the forecasts from 2005 through 2009, compare the accuracy of each of the forecasting methods based on the RMSE criterion. Which forecast would you have used for 2010? Why?
- Suppose, as an economist, you are asked to analyze an issue unlike anything you have ever done before. Also, suppose you do not have a specific model for analyzing that issue. What should you do? Hint: What would a carpenter do in a similar situation?Furniture Forecasting Futura Furniture Products manufactures upscale office furniture for the Office of the Future. The sales division comprises regionally based sales offices made up of sales representatives and regional managers. Sales representativeswho report to the regional managersconduct direct sales efforts with customers in their regions. As part of the sales process, representatives gather information about likely future orders and convey that information back to the regional managers. Regional managers use that information to create sales forecasts, which are then used as the basis for manufacturing schedules. Sales representatives and regional managers are both compensated on a salary plus commission (percentage of revenue as pricing is centrally controlled). However, a regional managers commission is adjusted based on regional sales that exceed the forecasted budget. Corporate managers are concerned with one of Futuras key products, the DeskPod. They worry that DeskPod forecasts are inaccurate, causing extreme havoc in the manufacturing process. How are the forecasts likely to be inaccurate? What do you think is driving this inaccuracy? How might this problem be solved?List some arguments for and against the likelihood of convergence.
