ISQA 459/559 Advanced Forecasting Mellie Pullman
30 Recall Forecast Error Measurements MFE: mean forecast error MAD: mean absolute deviation
Best Error Measurement (What it the problem with the MAD calculation as an error measurement for long histories?) 365 days Averaged ?
Solution? Smoothed MAD Phi () is a smoothing parameter, which is set in advance. It is important that we fix (set) phi BEFORE we try to find the best forecasting method. Why?
Phi Phi controls the period of time over which we are evaluating forecast accuracy--the smaller the value of phi, the larger the number of historical periods that are considered in the measurement of the "average" forecast error. What effect would changing phi have while you are trying to compare the accuracy of two different forecasting methods?
Suggested Values for Phi Forecasting IntervalGood Values of Phi Daily.02 (149 days).03 (99 days).04 (74 days).05 (59 days).10 (29 days) Weekly.05 (59 weeks).10 (29 weeks).15 (19 weeks).20 (14 weeks) Monthly.10 (29 months).15 (19 months).20 (14 months).25 (11 months).30 (9 months)
Phi0.3 MonthDemandForecast ErrorMAD TOTALS
QuarterYear 1Year 2Year 3Year Total Average Seasonal Index/Factor We estimate 2600 for Year 5 but need to know how many to make each quarter.
Seasonal Factor Method
QuarterYear 1Year 2Year 3Year 4 145/250 = Total Average Seasonal Index = = Seasonal Index/Factor
Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal Index 1( )/4 = ( )/4 = ( )/4 = ( )/4 = 0.50 Seasonal Index/Factor
Quarter Year 1 Year 2 Year 3 Year 4 145/250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = /250 = /300 = /450 = /550 = 0.39 QuarterAverage Seasonal IndexForecast 1( )/4 = (0.20) =130 2( )/4 = (1.30) =845 3( )/4 = (2.00) =1300 4( )/4 = (0.50) =325 Seasonal Influences
In- Class Problem: Forecast Year 3 (Overall forecast = 1500) Qtr Year 1Year 2 Average Index DemandIndexDemandIndex Avg
Decomposition of Season & Trend Decompose the data into components Find seasonal component Deseasonalize demand Find Trend component Forecast future values of each component Project Trend component into future Multiply trend component by seasonal component
Example of Deseasonalized Data
Project Future and Re-seasonalize
Options for Brewery Case that use regression and/or seasonal adjustment? Using Yearly Data to start? Using Monthly data to start?
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Actual room requests
Trend-Adjusted Exponential Smoothing
||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Guest Arrivals A t = D t + (1 - )(A t-1 + T t-1 ) T t = (A t - A t-1 ) + (1 - )T t-1
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week A 1 = 0.2(27) (28 + 3)= 30.2 T 1 = 0.2( ) (3)= 2.8 Guest Arrivals A 0 = 28 g D 1 = 27 g T 0 = 3 g = 0.20 = 0.20 A t = D t + (1 - )(A t-1 + T t-1 ) T t = (A t - A t-1 ) + (1 - )T t-1
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week A 1 = 30.2 T 1 = 2.8 Guest Arrivals A 0 = 28 guests T 0 = 3 guests = 0.20 = 0.20 A t = D t + (1 - )(A t-1 + T t-1 ) T t = (A t - A t-1 ) + (1 - )T t-1 Forecast 2 = = 33
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Guest Arrivals A 1 = 30.2 D 2 = 44 T 1 = 2.8 = 0.20 = 0.20 A t = D t + (1 - )(A t-1 + T t-1 ) T t = (A t - A t-1 ) + (1 - )T t-1 A 2 = T 2 = Forecast =
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Guest Arrivals A 1 = 30.2 D 2 = 44 T 1 = 2.8 = 0.20 = 0.20 A t = D t + (1 - )(A t-1 + T t-1 ) T t = (A t - A t-1 ) + (1 - )T t-1 A 2 = 35.2 T 2 = 3.2 Forecast = = 38.4
Trend-Adjusted Exponential Smoothing ||||||||||||||| — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Trend-adjusted forecast Actual guest arrivals
In Class Exercise A mar = 300,000 cases; T mar = +8,000 cases D apr = 330,000 cases; = 0.20 =.10 What are the forecasts for May and July?
The End