FORECASTINGMETHODSFORSEASONALSERIESOutlineMultiplicativeSeasonalInfluences.AdditiveSeasonalInfluencesSeasonal influencewithtrend
Outline • Multiplicative Seasonal Influences • Additive Seasonal Influences • Seasonal influence with trend FORECASTING METHODS FOR SEASONAL SERIES
Turkeys have a long-term trend for increasing demand with aseasonal pattern. Sales are highest during September toNovember and sales are lowestduring December andJanuary
Turkeys have a long-term trend for increasing demand with a seasonal pattern. Sales are highest during September to November and sales are lowest during December and January
Seasonal InfluencesYear 4QuarterYear1Year2Year3145701001002335370585725352059083011604100170285215Total2200100012001800250300450550AverageConsider the demand data shown above. Is the dataseasonal? Are the demands in Quarter 1 consistently lessthan the average? What is the relationship of Quarter 1demand with the average? How about the other quarters?
Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 Seasonal Influences Consider the demand data shown above. Is the data seasonal? Are the demands in Quarter 1 consistently less than the average? What is the relationship of Quarter 1 demand with the average? How about the other quarters?
Seasonallnfluences Is it not true that Quarter 1 demand is less than theaverage? How much less do you expect the Quarter 1demand fromthe average?: One can take different approaches to answer this question- Answer 1: Quarter 1 demand is approximately 20% ofthe average.- Answer 2: Quarter 1 demand is approximately 200 unitsless than the averageAre these answers true? We shall verify the correctness ofthe answers in this lesson. The first answer uses theconcept of multiplicative seasonal influence and the secondanswer additive seasonal influence.We shall now definethesetwo seasonalinfluences
Seasonal Influences • Is it not true that Quarter 1 demand is less than the average? How much less do you expect the Quarter 1 demand from the average? • One can take different approaches to answer this question. – Answer 1: Quarter 1 demand is approximately 20% of the average. – Answer 2: Quarter 1 demand is approximately 200 units less than the average. • Are these answers true? We shall verify the correctness of the answers in this lesson. The first answer uses the concept of multiplicative seasonal influence and the second answer additive seasonal influence. We shall now define these two seasonal influences
Seasonal lnfluences: A seasonal influence is multiplicative ifthe quarterly demand forecast of a quarter= projected average quarterly demandx average seasonal index of that quarter. A seasonal influence is additive ifThe quarterly demand forecast of a quarter= projected average quarterly demand+ average seasonal index of that quarter
Seasonal Influences • A seasonal influence is multiplicative if the quarterly demand forecast of a quarter = projected average quarterly demand average seasonal index of that quarter. • A seasonal influence is additive if The quarterly demand forecast of a quarter = projected average quarterly demand + average seasonal index of that quarter
Multiplicative Seasonal InfluencesYear 1Year 2Year 3Year 4Quarter145/250=0.1870/300=0.23100/450=0.22100/550=0.182335/250=1.34370/300=1.23585/450=1.30725/550=1.323520/250=2.08590/300=1.97830/450=1.841160/550=2.114100/250=0.40170/300=0.57285/450=0.63215/550=0.39Multiplicative influenceStep 1: For each period, computeActual Quarterly DemandSeasonal index :Average Quarterly DemandFor example, seasonal Index, Year 1, Quarter 1=
Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Multiplicative Seasonal Influences For example, seasonal Index, Year 1, Quarter 1 = Seasonal index = Actual Quarterly Demand Average Quarterly Demand Step 1: For each period, compute Multiplicative influence:
Multiplicative Seasonal InfluencesYear 1Year 2QuarterYear 3Year 4145/250=0.1870/300=0.23100/450=0.22100/550=0.182335/250=1.34370/300=1.23585/450=1.30725/550=1.323520/250=2.08590/300=1.97830/450=1.841160/550=2.114100/250=0.40170/300=0.57285/450=0.63215/550=0.39QuarterAverageSeasonalIndexStep 2: For1each quarter2computethe3average4seasonal index
Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39 Quarter Average Seasonal Index 1 2 3 4 Multiplicative Seasonal Influences Step 2: For each quarter compute the average seasonal index
Multiplicative Seasonal InfluencesThe average seasonal indices can be used to get forecastsof the quarterly demands if the average quarterly demand isprojected. The quarterly demand forecast of a quarter =projected average quarterly demand x average seasonalindex of that quarter.For example, suppose that the next year, in Year 5The projected annual demand is 2600. So, the projectedaverage quarterly demand is 2600/4=650.Then, the demand forecast in Quarter 1 = 650(0.20)=130. Thenext slide shows the demand forecast for the other quarters
Multiplicative Seasonal Influences The average seasonal indices can be used to get forecasts of the quarterly demands if the average quarterly demand is projected. The quarterly demand forecast of a quarter = projected average quarterly demand average seasonal index of that quarter. For example, suppose that the next year, in Year 5, The projected annual demand is 2600. So, the projected average quarterly demand is 2600/4=650. Then, the demand forecast in Quarter 1 = 650(0.20)=130. The next slide shows the demand forecast for the other quarters
Multiplicative Seasonal InfluencesGiven projected average quarterly demand =650The quarterly demand forecasts are obtained as follows:QuarterAverage Seasonal IndexForecast1234
Multiplicative Seasonal Influences Given projected average quarterly demand =650 The quarterly demand forecasts are obtained as follows: Quarter Average Seasonal Index Forecast 1 2 3 4
Additive SeasonallnfluencesYear 1Year 2Year 3Year 4Quarter145-250=-20570-300=-230100-450=-350100-550=-4502335-250=85370-300=70585-450=135725-550=1753520-250=270590-300=290830-450=3801160-550=6104100-250=-150170-300=-130285-450=-165215-550=-335Additiveinfluence:Step 1: For each period, compute seasonal index= Actual Quarterly Demand - Average Quarterly DemandForexample, seasonal Index, Year 1,Quarter 1=45-250=-205
Additive Seasonal Influences For example, seasonal Index, Year 1, Quarter 1 = 45-250 = -205 = Actual Quarterly Demand - Average Quarterly Demand Step 1: For each period, compute seasonal index Additive influence: Quarter Year 1 Year 2 Year 3 Year 4 1 45-250 = -205 70-300 = -230 100-450 = -350 100-550 = -450 2 335-250 = 85 370-300 = 70 585-450 = 135 725-550 = 175 3 520-250 = 270 590-300 = 290 830-450 = 380 1160-550 = 610 4 100-250 = -150 170-300 = -130 285-450 = -165 215-550 = -335