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Deseasonalizing Deseasonalizing ForecastsForecasts
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Agenda:Agenda:• Seasonality defined & seasonal adjustment
methods• Brainstorming Exercise• Nuts and Bolts• How It Works• Seasonal adjustment example• Exercise• Summary• Appendix A: Solution to Exercise
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SeasonalitySeasonality• A repeated pattern of spikes or drops
in the variable of interest associated with a period of time
• Examples-– Consumer buying habits– Price of gasoline
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SeasonalitySeasonality• Causes of seasonal movement by
class:1. Weather (temperature, precipitation)2. Calendar Events (religious or secular festivals)3. Timing decisions (vacations, accounting periods)
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Seasonal Adjustment Seasonal Adjustment MethodsMethods
• Seasonal index
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Nuts and BoltsNuts and BoltsWhy make seasonal adjustments?
– Reduces errors in time-series forecasting– Improves quality of judgmental forecasts– Gives good insight into the factors influencing
demand
The purpose of finding seasonal indexes is to remove the seasonal effects from the time series
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How It Works: How It Works: Deseasonalizing ForecastsDeseasonalizing Forecasts
Four-step procedure for seasonal adjustments:
1. Calculate forecast for each demand values in the time series
2. For each demand value, calculate Demand/Forecast
3. Average the Demand/Forecast for months or quarters to get the seasonal index
4. Multiply the unadjusted forecast by the seasonal index to find adjusted forecast value
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Season Adjustment ExampleSeason Adjustment Example• Foster Company makes widgets.
The quarterly demand for its widget is given in Exhibit 1
• Using linear regression forecasting, develop a seasonal index for each quarter and reforecast each quarter
Year Quarter Demand1 1 72
2 1103 1174 172
2 1 762 1123 1304 194
3 1 782 1193 1284 201
4 1 812 1343 1414 216
Exhibit 1
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Seasonal Adjustments ExampleSeasonal Adjustments ExampleStep 1Step 1
Calculate forecast for each demand values in the time series– Use the unadjusted regression forecast
modelY= a + bx
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Seasonal Adjustments Example – Seasonal Adjustments Example – Step 1Step 1
• Forecasted demandY=95.85+4.03*period
• Year 1 Quarter 1:Y=95.85+4.03(1)
=99.9
UnadjustedRegression
Period Year Quarter Demand Forecast1 1 1 72 99.92 2 110 103.93 3 117 107.94 4 172 112.05 2 1 76 116.06 2 112 120.07 3 130 124.18 4 194 128.19 3 1 78 132.1
10 2 119 136.211 3 128 140.212 4 201 144.213 4 1 81 148.214 2 134 152.315 3 141 156.316 4 216 160.3
Exhibit 2
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Seasonal Adjustments Example – Seasonal Adjustments Example – Step 2Step 2
• For each demand value, calculate Demand/Forecast
• Year 1 Quarter 1:72/99.9= 0.72
UnadjustedRegression Demand/
Period Year Quarter Demand Forecast Forecast1 1 1 72 99.9 0.722 2 110 103.9 1.063 3 117 107.9 1.084 4 172 112.0 1.545 2 1 76 116.0 0.666 2 112 120.0 0.937 3 130 124.1 1.058 4 194 128.1 1.519 3 1 78 132.1 0.59
10 2 119 136.2 0.8711 3 128 140.2 0.9112 4 201 144.2 1.3913 4 1 81 148.2 0.5514 2 134 152.3 0.8815 3 141 156.3 0.9016 4 216 160.3 1.35
Exhibit 3
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Seasonal Adjustments Example - Seasonal Adjustments Example - Step 3Step 3
• Average the Demand/Forecast for the quarters to get the seasonal index
• Quarterly Seasonal Index for Quarter 1:(0.72+0.66+0.59+0.55)/4 =
0.63
QuarterlyDemand/ Seasonal
Period Year Quarter Forecast Index1 1 1 0.72 0.632 2 1.06 0.943 3 1.08 0.994 4 1.54 1.455 2 1 0.66 0.636 2 0.93 0.947 3 1.05 0.998 4 1.51 1.459 3 1 0.59 0.6310 2 0.87 0.9411 3 0.91 0.9912 4 1.39 1.4513 4 1 0.55 0.6314 2 0.88 0.9415 3 0.90 0.9916 4 1.35 1.45
Exhibit 4
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Seasonal Adjustments Example - Seasonal Adjustments Example - Step 4Step 4
• Multiply the unadjusted forecast by the seasonal index to find the adjusted forecast values
• Year 1 Quarter 1:99.9 * 0.63 = 62.7 (adjusted forecast)
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Seasonal Adjustments Example - Seasonal Adjustments Example - Step 4Step 4
Unadjusted Quarterly AdjustedRegression Demand/ Seasonal Regression
Period Year Quarter Demand Forecast Forecast Index Forecast1 1 1 72 99.9 0.72 0.63 62.72 2 110 103.9 1.06 0.94 97.33 3 117 107.9 1.08 0.99 106.54 4 172 112.0 1.54 1.45 162.15 2 1 76 116.0 0.66 0.63 72.96 2 112 120.0 0.93 0.94 112.47 3 130 124.1 1.05 0.99 122.48 4 194 128.1 1.51 1.45 185.59 3 1 78 132.1 0.59 0.63 83.010 2 119 136.2 0.87 0.94 127.511 3 128 140.2 0.91 0.99 138.312 4 201 144.2 1.39 1.45 208.813 4 1 81 148.2 0.55 0.63 93.114 2 134 152.3 0.88 0.94 142.615 3 141 156.3 0.90 0.99 154.216 4 216 160.3 1.35 1.45 232.1
Exhibit 5
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Seasonal Adjustments Seasonal Adjustments ExampleExample
Unadjusted Regression Forecast
0
50
100
150
200
250
1 3 5 7 9 11 13 15
Period
Dem
and Demand
UnadjustedForecast
Seasonality Adjusted Forecast
0
50
100
150
200
250
1 3 5 7 9 11 13 15
Period
Dem
and
Demand
AdjustedForecast
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ExerciseExercise• Smith Company makes widgets.
The quarterly demand for its widget is given in Exhibit A
• You have been asked to develop a seasonal index for each quarter and reforecast each quarter
Year Quarter Demand1 1 20
2 9.23 33.24 40
2 1 33.22 243 46.84 53.2
Exhibit A
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Exercise TableExercise Table
Unadjusted Quarterly AdjustedRegression Demand/ Seasonal Regression
Period Year Quarter Demand Forecast Forecast Index Forecast1 1 1 20 16.4 1.22 1.09 17.82 2 9.2 21.0 0.44 0.52 11.03 3 33.2 25.6 1.30 1.18 30.24 4 40 30.2 1.33 1.21 36.55 2 1 33.2 34.8 0.95 1.09 37.86 2 24 39.4 0.61 0.52 20.67 3 46.8 44.0 1.06 1.18 51.98 4 53.2 48.6 1.10 1.21 58.8
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SummarySummary• Deseasonalizing forecasts is effective
for– Short-term forecasting– Comparability– Detecting trend changes early
• The Seasonal Index is the most simple method for making seasonal adjustments
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Appendix A: Solution to Appendix A: Solution to ExerciseExercise
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.779
R Square 0.607
Adjusted R Square 0.541
Standard Error 9.787
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 886.881 886.881 9.259 0.023
Residual 6 574.699 95.783
Total 7 1461.580
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 11.771 7.626 1.544 0.174 -6.888 30.431 -6.888 30.431
X Variable 1 4.595 1.510 3.043 0.023 0.900 8.290 0.900 8.290
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Appendix A: Solution to Appendix A: Solution to ExerciseExercise
Unadjusted Quarterly AdjustedRegression Demand/ Seasonal Regression
Period Year Quarter Demand Forecast Forecast Index Forecast1 1 1 20 16.4 1.22 1.09 17.82 2 9.2 21.0 0.44 0.52 11.03 3 33.2 25.6 1.30 1.18 30.24 4 40 30.2 1.33 1.21 36.55 2 1 33.2 34.8 0.95 1.09 37.86 2 24 39.4 0.61 0.52 20.67 3 46.8 44.0 1.06 1.18 51.98 4 53.2 48.6 1.10 1.21 58.8