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A forecasting project for an economics course at the Schulich School of Business
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Sales Forecasting
Jeric (Jose) Kison
BACKGROUND
Microsoft’s Quarterly Sales
Seasonality
FORECASTING
Winter’s Method
Winter’s Method
Quarter Actual sales Forecasted Sales
Q3 2010 $ 14,503,000,000 $15,599,000,000
Q4 2010 $ 16,039,000,000 $15,961,700,000
Q1 2011 $ 16,195,000,000 $15,702,300,000
Q2 2011 $ 19, 953,000,000 $19,043,100,000
Q3 2011 - $16,652,900,000
Q4 2011 - $17,022,300,000
Parabolic Trend
Parabolic Trend
Quarter Actual sales Forecasted Sales
Q3 2010 $ 14,503,000,000 $16,659,400,000
Q4 2010 $ 16,039,000,000 $16,999,300,000
Q1 2011 $ 16,195,000,000 $17,342,100,000
Q2 2011 $ 19, 953,000,000 $17,687,800,000
Q3 2011 - $16,659,400,000
Q4 2011 - $16,999,300,000
ARIMA
ARIMAModel: ARIMA(1,0,0)(1,1,0)4
Final Estimates of ParametersFinal Estimates of Parameters
Type Coef SE Coef T PType Coef SE Coef T PAR 1 0.4066 0.1364 2.98 0.004AR 1 0.4066 0.1364 2.98 0.004SAR 4 -0.7263 0.1218 -5.96 0.000SAR 4 -0.7263 0.1218 -5.96 0.000Constant -0.01581 0.01656 -0.95 0.344Constant -0.01581 0.01656 -0.95 0.344
Differencing: 0 regular, 1 seasonal of order 4Differencing: 0 regular, 1 seasonal of order 4Number of observations: Original series 56, after differencing 52Number of observations: Original series 56, after differencing 52Residuals: SS = 0.693955 (backforecasts excluded)Residuals: SS = 0.693955 (backforecasts excluded) MS = 0.014162 DF = 49MS = 0.014162 DF = 49
Modified Box-Pierce (Ljung-Box) Chi-Square statisticModified Box-Pierce (Ljung-Box) Chi-Square statistic
Lag 12 24 36 48Lag 12 24 36 48Chi-Square 14.3 18.1 40.8 51.4Chi-Square 14.3 18.1 40.8 51.4DF 9 21 33 45DF 9 21 33 45P-Value P-Value 0.112 0.642 0.164 0.2370.112 0.642 0.164 0.237
Final Estimates of ParametersFinal Estimates of Parameters
Type Coef SE Coef T PType Coef SE Coef T PAR 1 0.4066 0.1364 2.98 0.004AR 1 0.4066 0.1364 2.98 0.004SAR 4 -0.7263 0.1218 -5.96 0.000SAR 4 -0.7263 0.1218 -5.96 0.000Constant -0.01581 0.01656 -0.95 0.344Constant -0.01581 0.01656 -0.95 0.344
Differencing: 0 regular, 1 seasonal of order 4Differencing: 0 regular, 1 seasonal of order 4Number of observations: Original series 56, after differencing 52Number of observations: Original series 56, after differencing 52Residuals: SS = 0.693955 (backforecasts excluded)Residuals: SS = 0.693955 (backforecasts excluded) MS = 0.014162 DF = 49MS = 0.014162 DF = 49
Modified Box-Pierce (Ljung-Box) Chi-Square statisticModified Box-Pierce (Ljung-Box) Chi-Square statistic
Lag 12 24 36 48Lag 12 24 36 48Chi-Square 14.3 18.1 40.8 51.4Chi-Square 14.3 18.1 40.8 51.4DF 9 21 33 45DF 9 21 33 45P-Value P-Value 0.112 0.642 0.164 0.2370.112 0.642 0.164 0.237
ARIMA
Quarter Actual sales Forecasted Sales
Q3 2010 $ 14,503,000,000 $12,925,265,037
Q4 2010 $ 16,039,000,000 $13,610,182,455
Q1 2011 $ 16,195,000,000 $12,848,267,877
Q2 2011 $ 19, 953,000,000 $19,419,519,788
Q3 2011 - $13,339,540,703
Q4 2011 - $13,747,055,400
Which has the best forecast?
Forecast summary statistics
Parabolic Trend
Winter’s Method
α = 0.5, β = 0.1, γ = 0.4
ARIMA (1,0,0)(1,1,0)4
MSD 9.71164E+17 8.03534E+17 4.97E+18
MAD 6.75902E+08 5.53333E+08 1.97E+09
MAPE 6.85693E+00 6.07142E+00 1.23E-01
Winter’s Method
Multivariable regression model
Variables to be used– US Economic Indicators
• GDP
• Personal Income
• Retail Sales
THANK YOU!
