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- 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.Choose one of the following forecasting methods discussed in this chapter: last-value, averaging, moving-average, or exponential smoothing. Identify the conditions when the method is most appropriate to use and give an example of an application of this method.Historical demand for Peeps is as displayed in the table. Month Demand January 11 February 18 March 31 April 39 May 44 June 53 July 67 August 82 September 96 Develop forecasts from June through October using these techniques: Holt's method with alpha=0.2 and beta=0.1. For Holt's model, the level and trend for May are assumed to be 44 and 12. Judge which forecast method is the best based on MAD.
- A researcher has a sample of 6 annual observations {94, 104, 102, 99, 111 and 107} for the CPI in country Z for the period 2015 to 2020, and wants to forecast CPI for the years 2021, 2022 and 2023. The researcher uses 3 different forecasting models: A, B and C. Model A is an AR(1) model with no drift and with an estimated autoregressive coefficient = 0.7. Model B is a MA(1) model with no constant and with an estimated MA coefficient = -0.4 (note the minus !). Model C is a random walk model with no drift. The error terms over the 2015-2020 period were estimated to have the values: {3, -1, 2, 4, -3, 1}. a. Compute the 2021, 2022 and 2023 forecasted values for the consumer price index based on the three models. Show the formulas and the details of your calculations, and explain all the related symbols. b. Suppose that the actual values of the CPI over the 2021, 2022 and 2023 were {108, 114, 105}. Calculate the Root mean square error of the three model forecasts over the 2021-2023…Two coincident indicators used in forecastingComprehensively state the criteria and process of selecting appropriate models for time series forecasting.
- Qualitative methods of forecasting include:a) sales force composite. b) jury of executive opinion.c) consumer market survey. d) exponential smoothing.e) all except (d).Use simple exponential smoothing with a = 0.6 to forecast the tire sales for September through December. Assume that the forecast for August was for 46 sets of tires. Do your forecasts seem to be biased? Why or why not? Month Sales August 53 September35 October 48 November 40Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows: Month Sales Forecast 1 Forecast 2 1 770 771 769 2 789 785 787 3 794 790 792 4 780 784 798 5 768 770 774 6 772 768 770 7 760 761 759 8 775 771 775 9 786 784 788 10 790 788 788 (a). Compute the MSE and MAD for each forecast. Does either forecast seem superior? Explain. (b). Compute MAPE for each forecast.