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1. The following is the yearly coffee production (in coded units) of a certain country from 2013 to 2021. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 t 1 2 3 4 5 6 7 8 9 21 31 29 32 16 Y 27 25 37 43 It is felt that the data can be fitted by the linear trend model, Y₁ = a + 3t+, where ~ NID(0,0²) and 3 > 0. (1) Here, ~ NID(0, 1) means ~ N(0, 1) for each t, and {e} are independent of each other at different times. (a) Find the least square estimates of a and 3, and forecast the value of 2022. [ (b) Instead of using least square estimate, it is suggested to use the Simple Expo- nential Smoothing (SES) method with exponential smoothing constant a = 0.1 and the initial forecast So = y₁ to construct 1-step ahead forecasts for the data, i.e. St = 0.1Y+0.9St-1- i. Calculate the one-step ahead forecast for the year 2015-2018. ii. Do you think SES overestimates or underestimates the model (1)? Briefly explain. iii. What do you suggest to improve the forecast and why?

1. The following is the yearly coffee production (in coded units) of a certain country from 2013 to 2021. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 t 1 2 3 4 5 6 7 8 9 21 31 29 32 16 Y 27 25 37 43 It is felt that the data can be fitted by the linear trend model, Y₁ = a + 3t+, where ~ NID(0,0²) and 3 > 0. (1) Here, ~ NID(0, 1) means ~ N(0, 1) for each t, and {e} are independent of each other at different times. (a) Find the least square estimates of a and 3, and forecast the value of 2022. [ (b) Instead of using least square estimate, it is suggested to use the Simple Expo- nential Smoothing (SES) method with exponential smoothing constant a = 0.1 and the initial forecast So = y₁ to construct 1-step ahead forecasts for the data, i.e. St = 0.1Y+0.9St-1- i. Calculate the one-step ahead forecast for the year 2015-2018. ii. Do you think SES overestimates or underestimates the model (1)? Briefly explain. iii. What do you suggest to improve the forecast and why?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 7E
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1. The following is the yearly coffee production (in coded units) of a certain country from 2013 to 2021. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 t 1 2 5 6 7 8 9 3 4 27 25 31 29 16 21 32 37 43 It is felt that the data can be fitted by the linear trend model, Yt Y₁ = a + 3t+ , where ~ NID(0,0²) and 3 > 0. EN Here, NID(0, 1) means ~ EN other at different times. (1) N(0, 1) for each t, and {e} are independent of each (a) Find the least square estimates of a and 6, and forecast the value of 2022. [ 1 (b) Instead of using least square estimate, it is suggested to use the Simple Expo- nential Smoothing (SES) method with exponential smoothing constant a = 0.1 and the initial forecast So = y₁ to construct 1-step ahead forecasts for the data, i.e. St = 0.1Y+0.9.St-1. i. Calculate the one-step ahead forecast for the year 2015-2018. ii. Do you think SES overestimates or underestimates the model (1)? Briefly explain. iii. What do you suggest to improve the forecast and why?
Transcribed Image Text:1. The following is the yearly coffee production (in coded units) of a certain country from 2013 to 2021. Year 2013 2014 2015 2016 2017 2018 2019 2020 2021 t 1 2 5 6 7 8 9 3 4 27 25 31 29 16 21 32 37 43 It is felt that the data can be fitted by the linear trend model, Yt Y₁ = a + 3t+ , where ~ NID(0,0²) and 3 > 0. EN Here, NID(0, 1) means ~ EN other at different times. (1) N(0, 1) for each t, and {e} are independent of each (a) Find the least square estimates of a and 6, and forecast the value of 2022. [ 1 (b) Instead of using least square estimate, it is suggested to use the Simple Expo- nential Smoothing (SES) method with exponential smoothing constant a = 0.1 and the initial forecast So = y₁ to construct 1-step ahead forecasts for the data, i.e. St = 0.1Y+0.9.St-1. i. Calculate the one-step ahead forecast for the year 2015-2018. ii. Do you think SES overestimates or underestimates the model (1)? Briefly explain. iii. What do you suggest to improve the forecast and why?
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