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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.Consider the following time series data: Month 1 2 3 4 5 6 7 Value 24 13 20 12 19 23 15 Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month 8? Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 8? Which method appears to provide the better forecast?21. Consider a firm subject to quarter-to-quarter variation in its sales. Suppose that the following equation was estimated using quarterly data for the period 2011–2018 (the time variable goes from 1 to 32). The variables D1, D2, and D3 are, respectively, dummy variables for the first, second, and third quarters (e.g., D1 is equal to 1 in the first quarter and 0 otherwise). Qt =a+bt+c1D1+c2D2+c3D3 The results of the estimation are presented here: a. Calculate the intercept in each of the four quarters. What do these values imply? b. Use this estimated equation to forecast sales in the fourth quarter of 2019.
- 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…5 True/False/uncertain 7) With all observations in the same cluster, RSQ = 1. 8) With 500 multiple imputation samples generating 500 predictions of 0 or 1 for the binary dependent variable for each observation, to combine the 500 predictions into one for each observation, one has to take the mean of all 500 predictions and use a cutoff of 50%.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. In the Bayside Fountain Hotel problem, compute an exponentially smoothed forecast with an α value of .20. According to the result from Excel and/or POM-QM, the forecast for the year 10 would be b. In the Bayside Fountain Hotel problem, for the exponentially smoothed forecast with an α value of .20, compute the mean absolute deviation (MAD) via Excel and/or POM-QM. c. In the Bayside Fountain Hotel problem, compute an adjusted exponentially smoothed forecast with α = .20and β = .20. According to the result from Excel and/or POM-QM, the forecast for the year 4 would be d.Suppose that you work for a U.S. senator who is contemplating writing a bill that would put a national sales tax in place. Because the tax would be levied on the sales revenue of retail stores, the senator has asked you to prepare a forecast of retail store sales for year 8, based on data from year 1 through year 7. The data are: (c1p2) Year Retail Store Sales 1 $1,225 2 1,285 3 1,359 4 1,392 5 1,443 6 1,474 7 1,467 54 Chapter One a. Use the first naive forecasting model presented in this chapter to prepare a forecast of retail store sales for each year from 2 through 8. b. Prepare a time-series graph of the actual and forecast values of retail store sales for the entire period. (You will not have a forecast for year 1 or an actual value for year 8.) c. Calculate the root-mean-squared error for your forecast series using the values for year 2 through year 7. 3. Use the second naive forecasting model presented in this chapter to answer parts (a) through (c) of Exercise 2. Use P 0.2 in…Suppose the relationship between Y and X is given by: Y = 3.1415 + 6X + error By how much does the expected value of Y change if X increases by 7.23 units? (Round your answer to two decimal places: ex: 123.45)
- 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.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?In the past four years, the annual returns of one company’s stockare 12%, 18%, and –14%, and 7%.a) What is the geometric average return? b) What is the arithmetic average of the returns? c) According to an economist’ forecast on the Year 2020, the probabilities of repeatingthe performances of the former four years are 30%, 30%, 20%, and 20%, respectively.What is the expected return of the stock in the Year 2020