Deseasonalizing Deseasonalizing ForecastsForecasts

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

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

SeasonalitySeasonality• Causes of seasonal movement by

class:1. Weather (temperature, precipitation)2. Calendar Events (religious or secular festivals)3. Timing decisions (vacations, accounting periods)

Seasonal Adjustment Seasonal Adjustment MethodsMethods

• Seasonal index

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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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