Consider the following time series data.O(a) Construct a time series plot.123Month 1 2 34Value56307252015105030Month252015105001 2 30124 13 20 12 19 23Compute MSE.MSE 20.55What type of pattern exists in the data?The data appear to follow a horizontal pattern.O The data appear to follow a seasonal pattern.O The data appear to follow a trend pattern.O The data appear to follow a cyclical pattern.2413201219+223+315MonthMonth1944164 5 6 7 81918.335 65Forecast(b) Develop the three-month moving average forecasts for this time series.Time SeriesValueXWhat is the forecast for month 8?19.33XX+6X7X7158Im15+DO30✓2520105-00 1 230252015-10-50013 4 5 6 7 8Month2 3 4Month5678@ (c) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)Time SeriesValueMonth1234567Month241132203124195236157Compute MSE. (Round your answer to two decimal places.)MSE 11XWhat is the forecast for month 8? (Round your answer to two decimal places.)20.30X(d) Compare the three-month moving average approach with the exponential smoothing approach using a = 0.2. Which appearsto provide more accurate forecasts based on MSE?[Submit AnswerO The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the three-monthmoving average.O The exponential smoothing using a = 0.2 provides a better forecast since it has a smaller MSE than the three-monthmoving average.● The three-month moving average provides a better forecast since it has a smaller MSE than the exponentialsmoothing using a = 0.2.Time SeriesValue24O The three-month moving average provides a better forecast since it has a larger MSE than the exponential smoothingusing a = 0.2.24Forecast(e) Use a smoothing constant of a = 0.4 to compute the exponential smoothing forecasts. (Round your answers to two decimalplaces.)1313202012121917.6232315Need Help? Read ItXXX24XX18.501917.2517.623ForecastXXXDoes a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.O The exponential smoothing using a = 0.2 provides a better forecast since it has a smaller MSE than the exponentialsmoothing using a = 0.4.XO The exponential smoothing using a = 0.4 provides a better forecast since it has a smaller MSE than the exponentialsmoothing using a = 0.2.O The exponential smoothing using a = 0.4 provides a better forecast since it has a larger MSE than the exponentialsmoothing using a = 0.2.O The exponential smoothing using a = 0.2 provides a better forecast since it has a larger MSE than the exponentialsmoothing using a = 0.4.webassign.net

Times series analysis is used to predict the variables based on the time. In a time series, it has…

Answered: Consider the following time series…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A statistical program is recommended. Suppose the following data shows a company's annual revenue from 2008 (period 1) to 2017 (period 10) in billions of dollars. ● Year Period 2008 2009 2010 T₂= 2011 2012 2013 2014 2015 2016 2017 120 100 80- 60 40 20 1 0 2 3 3 4 (a) Construct a time-series plot. 5 6 7 9 10 Annual Revenue ($ billions) $22.80 $24.65 $28.32 $37.91 $50.18 $54.50 $66.00 $73.99 $90.27 $110.86 01 1 2 3 4 5 6 7 8 9 10 11 Period What type of pattern exists? O The time series plot shows a horizontal pattern. O The time series plot indicates a linear pattern. O The time series plot shows a cyclical pattern. The time series plot indicates curvature in the data. 0 120 100 80+ 60 40 20- 0 0 1 2 3 5 6 7 8 9 10 11 Period 45 (b) Develop a quadratic trend equation. (Round your numerical values to four decimal places.) 120T 100 80 60 40 20+ 0 01 1 2 3 4 5 6 7 8 9 10 11 Period ✔ 120 100 80 60 40- 20+ 0 0 1 2 3 4 5 6 7 8 9 10 11 Period 0
Hudson Marine provides boats sales, service, and maintenance. Boat trailers are one of its top sales items. Suppose the quarterly sales values for the seven years of historical data are as follows. Do not round intermediate calculations. a. Compute the centered moving average values (first find Four-Quarter Moving Average) for this time series (to 3 decimals). Centered Moving Average t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Sales 5 17 8 6 9 16 16 7 14 24 22 12 18 26 26 20 24 33 28 23 22 36 29 18 28 42 33 28 9.625 Year 1 2 3 4 5 6 7 Quarter 1 5 9 14 18 24 22 28 Quarter 2 17 16 24 26 33 36 42 Quarter 3 B 16 22 26 28 29 33 Quarter 4 6 7 12 20 23 18 28 Total Yearly Sales 36 48 72 90 108 105 131
Centerville Bikes and Stuff (CBS) sells motorcycles and accessories. The number of helmets sold by CBS per week for the past six weeks follows. Week 1 2 3 4 5 6 Value 17 12 14 10 16 13 (a) Construct a time series plot. A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect are as follows. The segments start at (1, 17), go down and right to (2, 12), go up and right to (3, 14), go down and right to (4, 10), go up and right to (5, 16), and go down and right to stop at (6, 13). A graph has a horizontal axis labeled "Week" with values from 0 to 7 and a vertical axis labeled "Time Series Value" with values from 0 to 20. The time series plot contains a series of 6 points connected by line segments. The segments and the approximate points they connect…
Respond to each of the items using the following time series data. Period Demand 1 104 2 132 3 117 4 120 5 104 6 141 7 120 8 136 9 109 10 143 11 142 12 109 13 113 14 124 15 113 16 107
(b) Using statistical software, develop a linear trend equation for this time series to forecast revenue (in $ billions). (Round your numerical values to four decimal places.) T₂ = 2.8450+ - 0.0124 X (c) Use the trend equation developed in part (b) to forecast retail store revenue (in $ billions) for 2018. (Round your answer to one decimal place.) $34.1 billion
A statistical program is recommended. Annual retail store revenue for a technology company from 2007 to 2017 are shown below. Year Period 2007 Retail Store Revenue ($ billions) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 35 30 25 20 15 10 35 30 25 20 15 10 5- 0- 1 (a) Construct a time series plot. + 2 3 4 0 1 2 5 6 7 8 9 10 11 Retail Store Revenue ($ billions) 30 25 20 WML 15 10 0 1 2 3 4 5 6 7 8 9 10 11 12 Period 3.915 3 4 6.110 6.777 9.280 14.327 19.028 20.428 21.662 28.309 26.998 30.703 5 6 Period 7 8 9 10 11 12 What type of pattern exists in the data? The time series plot shows a cyclical pattern. The time series plot shows a horizontal pattern. O The time series plot shows a downward trend. The time series plot shows an upward trend. o Retail Store Revenue ($ billions) 35 35 30 25 20 15 10 0 1 2 3 4 5 6 7 8 9 10 11 12 Period VV 5- 0- 0 1 2 3 4 5 6 7 8 9 10 11 12 Period A (b) Using statistical software, develop a linear trend equation for this time series to forecast revenue…
The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014. Year Period (t) Revenue ($ billions) 2009 23.6 2010 29.3 2011 37.9 2012 4 50.2 2013 59.9 2014 6 66.7 (a) Construct a time series plot. 80- 80 80 80 70 70 70 70 60 60 60 60 50 50 50 50 40 40 40 40 30 30- 30 30 20- 20 20 20 10 10 10- 10 1 2 3 4 5 6 7 0- 1 2 3 4 5 7 1 3 4 5 6 7 1 3 4 5 6 7 Period Period Period Period What type of pattern exists in the data? O The time series plot shows a downward linear trend. O The time series plot shows an upward linear trend. O The time series plot shows an upward curvilinear trend. O The time series plot shows a downward curvilinear trend. (b) Develop a linear trend equation for this time series to forecast revenue (in billions of dollars). (Round your numerical values to three decimal places.) T. = -18323.211 +9.131lt (c) What is the average revenue increase per year (in billions of dollars) that this company has been realizing? (Round your answer to three…
The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014. Year Period (t) Revenue ($ billions) 2009 23.8 2010 2 29.3 2011 3 38.0 2012 4 50.2 2013 59.8 2014 66.8 (a) Construct a time series plot. 80 T 80- 80- 80 T 70 70 70 70 60 60 60- 60 50 50- 50 0- 50- 40 40- 40 40 30 30 30 30 20 20 20 20 10 10 10 10- 0- 0- 1 3 4 5 6. 7. 1 2 3 4 5 6 7 0 1 2 3 4 6. 7 0 1 3 4 7 Period Period Period Perjod What type of pattern exists in the data? The time series plot shows a downward curvilinear trend. O The time series plot shows a downward linear trend. O The time series plot shows an upward curvilinear trend. O The time series plot shows an upward linear trend. (b) Develop a linear trend equation for this time series to forecast revenue (in billions of dollars). (Round your numerical values to three decimal places.) T: = (c) What is the average revenue increase per year (in billions of dollars) that this company has been realizing? (Round your answer to three…
3. Compute three-period moving average and forecasting errors for the following time series: Period (t): 1 2 | 3 4 5 6 7 89 Value (X:): 15 27 20 14 25 11 20 25 18
The number of users of a certain website (in millions) from 2004 through 2011 follows. Year Period Users (Millions) 2004 1 1 2005 2 5 2006 3 11 2007 4 59 2008 5 146 2009 6 360 2010 7 608 2011 8 846 (a) Construct a time series plot. -A time series plot contains a series of 8 points connected by line segments. The horizontal axis ranges from 0 to 10 and is labeled: Period. The vertical axis ranges from 0 to 900 and is labeled: Millions of Users. The first point is at approximately (1, 850). The rest are plotted from left to right at regular increments of 1 period in a downward, diagonal direction that becomes less steep as period increases. The last point is at approximately (8, 0). -A time series plot contains a series of 8 points connected by line segments. The horizontal axis ranges from 0 to 10 and is labeled: Period. The vertical axis ranges from 0 to 900 and is labeled: Millions of Users. The first point is at approximately (1, 0). The rest are…
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