Exercise 1. What can you observed in a time plot below? Explain each pattern observed. Is the series stationary? If not, why say so? 30 20 10 اماماساسالالرا۔ 1995 2000 2005 $ in million Figure 5. Timeplot of monthly antidiabetic drug sales in Australia, 1991-2008 Year 15 25
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Topic: BASIC TOOLS IN FORECASTING (time series analysis)
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- State the model used in time series analysis.(b) The following data represent the Coca-Cola's revenues (in $ hundred millions) during 2019-2022. Quarter 2019 2020 2021 2022 Oct-Dec Jan-Mar Apr-Jun Jul-Sep 44 56 55 49 45 53 54 49 41 54 53 48 45 57 58 52 (i) Plot the series in a line graph. Do you find any seasonal pattern? Calculate the seasonal index and interpret. (ii) Deseasonalized the data and fit a linear trend to the deseasonalized series. (iii)Obtain the deseasonalized forecasts and seasonal forecasts for 2023 revenues. In which quarter, the seasonal forecast has the most? The least? Is this logical? (iv) To estimate a regression model using seasonal binaries, set up a data set. If the estimated regression using seasonal binaries is given by Revenues = 48.31+ 0.12Time – 5.39 Qtr 1+ 5.74 Qtr 2+ 5.62 Qtr 3 Find the forecast the revenues for each quarter in 2023 and compare the forecasts in (iii).True or false: In a Time-series plot, the vertical axis represents time.
- Construct a time-series plot for the following number of customers shopping at a new mall during a given week. Day Number of Customers Monday Tuesday Wednesday Thursday Friday Saturday 525 540 469 500 586 64049- The increase or decrease in the movements of a time series is called ______________. a. Secular trend. b. Erratic Trend c. None d. Seasonal TrendStorrs 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?
- Consider the following annual progression of number of in-person customers of a store during January through the COVID years. Year Customers Growth rate 2019 576 2020 550 2021 100 2022 150 2023 600 2024 580 Find the “average” rate of growth of customers. What type of average would you use, so that if the growth were steady at that rate, you would end up with 580 customers in 2024? Also fill the blank spaces (except the top one) in the table with the appropriate growth rate (negative ok).For each of the following common patterns found in time series, identify a reasonableexample from the real-world that would likely exhibit this pattern.a. Horizontalb. Trendc. Seasonalityd. CyclicalParker is 50 and wants to retire in 15 years. His family has a history of living well into their 90s. Therefore, he estimates that he will live to age 95. He currently has a salary of $120,000 and expects that he will need about 65% of that amount annually at the beginning of each year if he were retired. He can earn 9 percent in his portfolio while he is working. However, he expects that he will only earn 7 percent in his portfolio during retirement. He expects inflation to continue at 3 percent. Parker currently has $350,000 invested for his retirement. His Social Security benefit in today’s dollars is $30,000 per year at normal age retirement of age 67. His Social Security benefit will be reduced by 6 2/3 percent for each year he begins collecting before full age retirement. How much does he need to save at the end of each year to meet his retirement goals (assume he does not wish to leave a financial legacy)?
- Calculate the approximate price relatives to two decimal places for the MTN and Vodacom stocks over the period in question. A. 0.71, 0.67 B. 0.57, 0.75 C. 0.75, 0.77 D. 0.70, 0.81What do you mean by Time Series Analysis?For each data series, (you can creat graph with year on x axis and data series on y axis to visually see if it appear stationary or not) carefully describe what appears to be happening over the period from 1982 to 2022, and why you think it is happening. Base your answer upon your knowledge of statistics and agriculture, along with common sense. If you are not entirely sure what is happening. In some cases what is happening in one graph may affect what you see in another. Dataset: Year Spring wheat seeded acreage Wheat cost of production ($/acre) Spring wheat yield (bushels/acre) Spring wheat production (bu per acre) Wheat price ($/ tonne) Canola production (tonnes) Canola price ($/ tonne) Canola Seeded acreage 1982 4,000,000 167.9 34 136,000 165 399,200 260 850,000 1983 4,600,000 153.3 27.2 125,300 174 397,000 383 950,000 1984 4,450,000 171.4 30.9 137,500 172 544,000 351 1,200,000 1985 4,850,000 166.6 39.6 192,000 156 635,000 263 1,000,000 1986 4,940,000 164.3 33.2…