Below you are given the seasonal indexes and the estimated trend equation for a time series. These values were computed on the basis of 2016 through 2020, 5 years of quarterly data. t = 1 for first quarter of 2016 t = 2 for second quarter of 2016 and so forth ....... Quarter Seasonal Index St 1 1.2 2 .9 3 .8 4 1.1 Tt = 126.23 + 1.6t
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- The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
- Table 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for January 2018 to December 2020 period: a. Calculate the Seasonal Index for every quarter. b. If the trend is described by the trend line T^ = 1,000 + 30 t, what is the forecast for the fourth quarter of 2021?For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. a. Compute for a 3 month moving average forecast. b. Compute for the exponential smoothing forecast for a=0.2. c. Which provides the better forecast using MSE as the measure of model accuracy? d. What is the forecast for next month?
- Show all your calculations where applicable. A hotel’s monthly occupancy rate (measured as a percentage of rooms available) is reported as follows for a nine (9)-month period: Months Sep Oct Nov Dec Jan Feb Mar Apr May Occupancy (%) 74 82 70 90 88 74 64 69 58 Calculate the trend line for the hotel occupancy rate data above. INSTRUCTION: You MUST make use one of the Time series formulae in the formulae sheet and the template below to obtain full marks: Occupancy rate (y) Months (x) x2 xyStorrs Cycles has just started selling the new Cyclonemountain bike, with monthly sales as shown in the table. First,co-owner Bob Day wants to forecast by exponential smoothingby initially setting February’s forecast equal to January’s saleswith a = .1. Co-owner Sherry Snyder wants to use a three-periodmoving average. a) Is there a strong linear trend in sales over time?b) Fill in the table with what Bob and Sherry each forecast forMay and the earlier months, as relevant.c) Assume that May’s actual sales figure turns out to be 405.Complete the table’s columns and then calculate the meanabsolute deviation for both Bob’s and Sherry’s methods.d) Based on these calculations, which method seems moreaccurate?For the following list of data (number of sold cars in every year ) , apply “exponential smoothing with trend” for all the years below. (i.e find the Forecast including trend) : Assume trend is zero for the 2012 years. ---- case1 use : α= 0.01 and β = 0.3 ---- case2 use: for α= 0.1 and β = 0.05 Calculate MAD for both cases Decide which case values are better and why? Year Number of sold cars 2012 110 2013 123 2014 160 2015 133 2016 151 2017 175 2018 189 2019 211 2020 255
- consider the following time series data.t 1 2 3 4 5 6 7yt10 9 7 8 6 4 4a. construct a time series plot. What type of pattern exists in the data?b. develop the linear trend equation for this time series.c. What is the forecast for t = 8?John Kittle, an independent insurance agent, uses a five-year moving average to forecast the number of claims made in a single year for one of the large insurance companies he sells for. He has just discovered that a clerk in his employ incorrectly entered the number of claims made four years ago as 1,400 when it should have been 1,200.a. What adjustment should Mr. Kittle make in next year’s forecast to take into account the corrected value of the number of claims four years ago?b. Suppose that Mr. Kittle used simple exponential smoothing with a = .2instead of moving averages to determine his forecast. What adjustment is now required in next year’s forecast? (Note that you do not need to know the value of the forecast for next year in order to solve this problem.)Which of the following time series forecasting methods would not be used to forecast seasonal data?