Assume the following AR(1) Y, = 0.036 + 0.69Y,-1 + E Suppose you have data for t-1, let's say Y,I = 3.4 %D a. Estimate the forecasts for Y,t -1, Y+1]t -1, Y+2|t - 1 b. if actual Y, = -0.032, Y+1 = 0.961, Y42 = 0.203. Find MSE?
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- 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?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.The following is the data of recent refrigerator sales at a local Home Depot store. Month 1 2 3 4 5Actual Sales 95 100 80 90 ???Inputs will be exact numbers. What is the forecasted sales in month 5 using naive approach.Please use a 2-month simple moving average method to forecast sales in month 5.Please use a weighted moving average method, with weights of 0.6 one period ago, 0.3 two periods ago, and 0.1 three periods ago, to forecast sales in month 5.
- Based on annual data from 2000-2010, the Gadget Company estimates that sales are growing according to a linear trend: Q = 50,000 + 200t where t is time and t = 0 in 2000. a. Forecast sales for 2013. b. Do you see any problems with this forecasting method?Identify and briefly describe the two general forecasting approaches.Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 days
- How Forecasts is compared with predicted values? why these both terms are different?Jan '20 0.68 Feb '20 0.76 Mar '20 1.6 Apr '20 1.47 May '20 0.98 Jun '20 1.18 Jul '20 3.59 Aug '20 3.33 Sept '20 4.31 Oct '20 3.84 Nov '20 6.97 Dec '20 7.7 Using data above please provide one qualitative and two quantitative (Simple and weighted moving average) monthly forecasts in the United States for the holiday season in 2021a. 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.
- 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…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?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?