University:
California State University, Northridge
Course:
BANA 607 | Introduction to Business Analytics
Academic year:

2024
Views:

400

Pages:

10
Author:

segullinnerh

Basic Predictive Analysis Basics of Time Series Analysis Exponential Smoothing Problems If you can look into the seeds of time, and say which grain will grow and which will not speak then unto me. William Shakespeare, 1564-1616. Exponential Smoothing- Two Formulas That are the same Ft +1 = Ft + α( At − Ft ) Ft +1 = Ft + αAt − αFt Ft +1 = (1 − α) Ft + αAt From This Period to the Next Period 1. Given an actual demand of 60 for a period when forecast of 70 was anticipated, and an alpha of 0.3, what would the forecast for the next period be using simple exponential smoothing? F = (1-0.3)(70)+0.3(60) = 67 2. You have been asked to forecast demand for a product using an exponential smoothing. The actual demand and forecast for year 2019 where 850 and 910, respectively. Compute the demand forecast for 2020 using a smoothing constant of 0.3. F = (1-0.3)(910)+0.3(850) = 892 3. Given the following demand. What is your forecast for period 4 using exponential smoothing and α=0.5? 1:(300), 2:(500), 3:(600). Ft+1 = (1-α)Ft+ α(At) Ft+1 = (1-0.5)Ft+ 0.5(At) Ft+1 = (1/2) Ft+ (1/2) (At) Ft+1 = (Ft+At)/2 F3 = (F2+A2)/2 F3 = (300+500)/2= 400 F4 = (F3+A3)/2 = (400+600)/2 = 500 α: Large or Small, 0.1, 0.2, 0.4 4. Is large α better or small α? We do not know. It depends on data. The best α is the one that minimizes our metric which may be MAD or MSE or MARD. Week Demand Forecast 1 2 3 4 5 6 7 8 200 250 175 186 225 285 305 190 200 200 205 202 200.4 202.9 211.1 220.5 α= 0.1 =B2 Ft for α= 200 =(1-$E$1)*C2+$E$1*B2 200.00 =(1-$E$1)*C3+$E$1*B3 210.00 =(1-$E$1)*C4+$E$1*B4 203.00 =(1-$E$1)*C5+$E$1*B5 199.60 =(1-$E$1)*C6+$E$1*B6 204.68 =(1-$E$1)*C7+$E$1*B7 220.74 =(1-$E$1)*C8+$E$1*B8 237.60 0.2 Ft for α= 0.4 200 200.00 220.00 202.00 195.60 207.36 238.42 265.05 MAD in Excel 5. The president of State University wants to forecast student enrollments for the next academic year based on the following historical data for the past 5 years. What is your forecast for next year using exponential smoothing with α = 0.4? t 1 2 3 4 5 α= At 15000 16000 18000 20000 21000 0.4 Ft 15000 15000 15400 16440 17864 19118.4 =B3 =(1-$C$1)*C3+$C$1*B3 =(1-$C$1)*C4+$C$1*B4 =(1-$C$1)*C5+$C$1*B5 =(1-$C$1)*C6+$C$1*B6 =(1-$C$1)*C7+$C$1*B7 |E| 0 1000 2600 3560 3136 2574 Forecast Mean Forecast StdDev 19118 2574 MAD 0 500 1200 1790 2059.2 Role of α 6. A forecast based on the previous forecast plus a percentage of the forecast error is: A) a naive forecast B) a simple moving average forecast C) a centered moving average forecast Ft+1 = (1-α)Ft+ α(At) D) an exponentially smoothed forecast E) an associative forecast Ft+1 = Ft+ α(At-Ft ) 7. In exponential smoothing forecasting, using large values of the smoothing coefficient α generates forecasts that are more: A) accurate B) responsive C) random D) stable Ft+1 = (1-α)Ft+ α(At) E) level Meaning of α - From Naïve to No Change 8. For what value of α, exponential smoothing becomes naïve method (Ft+1 = At)? A) α =0 Ft+1 = (1-α)Ft+ α(At) B) α =0.25 C) α =0.5 Ft+1 = (At) D) α =0.75 Ft+1 = (1-1)Ft+ 1(At) E) α =1 9. For what value of α, exponential smoothing becomes a straight line? A) α =0 B) α =0.25 Ft+1 = (1-α)Ft+ α(At) C) α =0.5 D) α =0.75 Ft+1 = Ft E) α =1 Ft+1 = (1-0)Ft+ 0(At) Change Alpha Value from 1 to 0 by 0.1 steps Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 At Ft 6464 7475 8237 9480 11642 11705 11837 13101 14194 15760 15667 14338 11816 14095 14001 14123 14599 15160 15352 15631 16887 17549 17090 1 6464 6464 7475 8237 9480 11642 11705 11837 13101 14194 15760 15667 14338 11816 14095 14001 14123 14599 15160 15352 15631 16887 17549 Change alpha from 1 to 0 by step of .1 20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0 1995 2000 2005 2010 2015 2020 2025 Finding α 10. Exponential smoothing is being used to forecast demand. The current forecast of 66 was 5 units larger than actual demand. The next forecast is 65. Compute α? F(t+1) = Ft + α (At-Ft) 65 66 +5 -5 65 = 66 + α (-5) 5α=1 α = 0.2 11. It can be mathematically proved that the Age of data in exponential smoothing is 1/α . The larger the α, the larger the number of periods in the moving average. True or false? Why? False α = 0.5  age of data is 2 periods. α = 0.2  age of data is 5 periods. α = 0.1  age of data is 10 periods. Age of Data 12. Given a forecast using a 6-period moving average. What is the average age of data? The last piece (newest piece) of data is only 1 period old. The first piece (oldest piece) of data in a 6-period moving average is 6 periods old. The average age of data is (1+6)/2 = 3.5 13. If the age of data in exponential smoothing is 1/ α, for what value of α, exponential smoothing performs close to a 6-period moving average? The age of data in a 6-period moving average is 3.5. The age of data in exponential smoothing is 1/ α. 1/ α = 3.5 α = 1/3.5 α = 0.29

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