图 2.8.Methods of Forecasting Trend Seasonal Series Summation Deseasonalized Period Demand MA(4) CMA BCMA Ratio SF Demand 10 18.8125 0.532 0.558 17.91 2 20 18.8125 1.063 1.062 18.84 18.25 3 26 18.5 1.405 1.413 18.40 18.75 4 17 19.125 0.889 0.967 17.59 19.5 5 12 18.25 20 0.600 0.558 21.49 20.5 6 23 18.75 21.125 1.089 1.062 21.66 21.75 7 30 19.5 20.5625 1.459 1.413 21.23 8 22 20.5 20.5625 1.070 0.967 22.76 21.75
Period Demand MA(4) CMA BCMA Ratio SF Deseasonalized Demand 1 10 18.8125 0.532 0.558 17.91 2 20 18.8125 1.063 1.062 18.84 18.25 3 26 18.5 1.405 1.413 18.40 18.75 4 17 19.125 0.889 0.967 17.59 19.5 5 12 18.25 20 0.600 0.558 21.49 20.5 6 23 18.75 21.125 1.089 1.062 21.66 21.75 7 30 19.5 20.5625 1.459 1.413 21.23 8 22 20.5 20.5625 1.070 0.967 22.76 21.75 2.8. Methods of Forecasting Trend Seasonal Series Summation
2.8.Winter's Method for Seasonal Problems Winter's Method The moving-average method requires that all seasonal factors be recalculated from scratch as new data become available. Winter's method is a type of triple exponential smoothing. Easy to update as new data become available Assumptions: Model of the form:D=(u+G)c,+ The length of the season is exactly N periods and the seasonal factors are the same each season and have the property that ∑c,=N
2.8. Winter’s Method for Seasonal Problems Winter’s Method • The moving-average method requires that all seasonal factors be recalculated from scratch as new data become available. • Winter’s method is a type of triple exponential smoothing. • Easy to update as new data become available. Assumptions: ► Model of the form: ► The length of the season is exactly N periods and the seasonal factors are the same each season and have the property that D Gc t tt t t c N
2.8.Winter's Method for Seasonal Problems Winter's Method (triple exponential smoothing) The series.The current level of deseasonalized series S, S,=(D,/c-N)+(1-)(S-1+G-) The trend G,=B(S,-S-1)+(1-B)G1 The seasonal factors c,=y(D,/S,)+(1-Y)c-N The forecast made in period t for any future period t+t is given by (assume that t <=N) F=(S,+G)C+-N If N<T<=2N,the seasonal factor would be cr2N If 2N<T <=3N,the seasonal factor would be crw and so on
2.8. Winter’s Method for Seasonal Problems Winter’s Method (triple exponential smoothing) ► The series. The current level of deseasonalized series St ► The trend. ► The seasonal factors ► The forecast made in period t for any future period t+ τ is given by (assume that τ <= N) If N < τ <= 2 N, the seasonal factor would be ct+ τ-2N If 2 N < τ <= 3 N, the seasonal factor would be ct+ τ-3N and so on 1 1 1 t t tN t t S Dc S G G SS G t tt t 1 1 1 c DS c t t t tN 1 F S Gc tt t t t N ,
2.8.Winter's Method for Seasonal Problems Initialization Procedure Assume that exactly two seasons of data are available;that is,2N data points.Suppose that the current period is t=0,so that the past observations are labeled Da,D.N2,...,Do Step 1:Calculate the sample means for the two seasons Step 2:Define the initial slope estimate G。=('-)/N Step 3:Set the initial value of the series S,=V+G[(N-1)/2]
2.8. Winter’s Method for Seasonal Problems Initialization Procedure Assume that exactly two seasons of data are available; that is, 2N data points. Suppose that the current period is t = 0, so that the past observations are labeled D-2N+1, D-2N+2 , … , D 0 ► Step 1: Calculate the sample means for the two seasons ► Step 2: Define the initial slope estimate ► Step 3: Set the initial value of the series 0 1 2 21 1 1 1 , N j j j N jN V DV D N N G VVN 0 21 SVG N 020 1 2