# Exponential Smoothing and One-step-ahead Forecasts

**Topics:**Exponential smoothing, Moving average, Time series analysis

**Pages:**3 (718 words)

**Published:**March 16, 2013

Solutions

Problem 1: Observations of the demand for a certain part stocked at a parts supply depot during the calendar year 1999 were Month January February March April May June Demand 89 57 144 221 177 280 Month July August September October November December Demand 223 286 212 275 188 312

a. Determine the one-step-ahead forecasts for the demand for January 2000 using 3-, 6-, and 12-month moving averages. b. Using a four-month moving average, determine the one-step-ahead forecasts for July through December 1999. c. Compute MAD, MSE, MAPE for the forecasts obtained in b. Solution: a. MA (3) forecast: 258.33 MA (6) forecast: 249.33 MA (12) forecast: 205.33 b. Month July August September October November December Forecast 205.50 225.25 241.50 250.25 249.00 240.25 Demand 223 286 212 275 188 312 Error -17.50 -60.75 29.50 -24.75 61.00 -71.75

c. MAD = 44.21 MSE = 2391.45 MAPE = 17.91%

EMIS 8348 Homework 1 – Part 1

Solutions

Problem 2: Observed weekly sales of ball peen hammers at the town hardware store over an eightweek period have been 14, 9, 30, 22, 34, 12, 19, 23. a. Suppose that three-week moving averages are used to forecast sales. Determine the one-step-ahead forecasts for weeks 4 through 8. b. Suppose that exponential smoothing is used with a smoothing constant of α = 0.15. Find the exponential smoothing forecasts for weeks 4 through 8. c. Based on the MAD, which method did better? Solution: a. Week 4 5 6 7 8 b. and c. You may start ES forecast from week 1 or start ES forecast from week 4 using MA(3) forecast for the first period. The following are the results for each of the cases. Starting ES forecast from week 1: Week 1 2 3 4 5 6 7 8 Demand 14 9 30 22 34 12 19 23 ES(.15) 14 14 13.25 15.76 16.70 19.29 18.20 18.32 MA(3) |Error|ES |Error|MA

MA(3) Forecast 17.67 20.33 28.67 22.67 21.67

17.67 20.33 28.67 22.67 21.67

6.24 17.30 7.29 0.80 4.68 7.263 MADES

4.33 13.67 16.67 3.67 1.33 7.934 MADMA

Based...

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