Business Forecasting (Decomposition &Soothing Model)


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Duke Shu, a Willamette MBA interested in business forecasting, data mining, and strategic marketing, uploaded a series of his works to "cast a brick to attract a jade"--hoping to hear more constructive, brilliant feedback from industrial experts while networking with them.

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Business Forecasting (Decomposition &Soothing Model)

  1. 1. Seasonal and Smoothing Methods Exercise (Target) Author: Duke Shu
  2. 2. I. Data Understanding  Linear growth trend  Consistent multiplicative seasonal pattern with an increasing variation. Sales peaks at Q4 every year through initial peak at 3,931 in 1993 Q4 to 10,786 in 2001 Q4  Cycles are not obvious, but there might be a slight curve in the long-term  Irregular components do not give much noise  The observations above hint that Multiplicative Holt- Winters Method may be a strongly suitable model in our consideration
  3. 3. II(1). Additive Analysis Quality: high R Square of 96.56%., but large MSD of 136350.Independence violation is indicated by residual autocorrelation, which signals lack of adequacy. Sales initiate at $2295 in 1993 Q1 and maintains an increase of $161.15 per quarter.
  4. 4. II (2). Multiplicative Decomposition Analysis Compared to Additive Decomposition, Multiplicative Decomposition model is a better fit. In terms of quality, multiplicative model has significantly smaller MSD (32924) compared to that of additive model(MSD=136350); R Square of multiplicative model (=99.17%) is also higher than that of additive (R Square=96.56%). However, Independence violation is indicated by a significant low-order residual autocorrelation, which represents lack of adequacy. Sales initiates at $2286.59 in 1993 Q1 and maintains consistent increase of $160.27 per quarter. It peaks in Q4 with 28% over the trend, troughs in Q1 12% below the trend.
  5. 5. III.A Simple Exponential SmoothingBased on the Solver result, we minimized MSD to be 275730.17, and got Alpha=0.30. Independence is violated by low-order autocorrelation. Thus the model violates the adequacy assumption.
  6. 6. III.B Simple Linear Trend Model The model initiates at $2286.59 and increases at $160.27 ( 7%) per quarter. The deseasonalized data exhibits statistically significant linear trend (P-values =0.000 for T-test and F-test are the same, because there is only one predictor in the model). Another quality indicator, R square has a very high value of 99%. Independence is slightly violated by low-order autocorrelation in the first two lags. The curvature in residual fit graph indicates that maybe a quadratic term needs to be considered. Normality, Constant variance assumptions appear to be violated. Thus the model seems not adequate.
  7. 7. III. C Holt’s Two-Parameter Linear Exponential Smoothing By minimizing MSD=8798.30 through Solver, we got Alpha=0.2675, Beta=0.3.Obviously accuracy is strong, because MSD is only 8798.29 and R square=99.69%. Adequacy is strongly reinforced by independence in autocorrelation. Although this model capture the linear trend, it ignores seasonality, which suggests us to consider Holt- Winter Method.Conclusion for Part III. Given the highestaccuracy and adequacy of model C amongthe model A, B, C, we decide to chose it asthe preferred model. Forecast is as follows:
  8. 8. IV. Multiplicative Winter’s MethodBy minimizing MSD=11151.93 through Solver, we got Alpha=0.2135, Beta=0.3, Gamma=0.05. This model initiates at$2586.2 in 1993 Q1 and maintains a slowly constant growth at the rate of $127.58 per quarter. Sales peaks at Q4 28.9%over trend and troughs 12.6% below trend. R square is fairly large and MSD is way smaller than those of previous models,which indicates a strong accuracy. Adequacy is strongly reinforced by strong white noise in ACF, which implies theadequacy of being independent and identically distributed, therefore no autocorrelation.
  9. 9. V. Seasonal Multiple Regression This model initiates at $2299.5 in 1993 Q1 and maintains a slowly constant growth at the rate of $160.9 per quarter. Sales peaks at Q4 $1522.6 over trend and troughs $645.5 below trend. Adequacy is slightly violated due to some noises in ACF. Spikes in Q4 and Q8, Q3, Q7, Q11 Seem to indicate seasonality in residuals.
  10. 10. VI. Log Seasonal Multiple RegressionThis model initiates at 7.9 (log scale) in 1993 Q1 and maintains a slowly constant growth at the rate of 0.03 (log scale) perquarter. Sales peaks at Q4 0.26 (log scale) over trend and troughs 0.12 (log scale) below trend. Independence violation isindicated by significant low-order residual autocorrelation, which shows a slightly weak adequacy. MSE in originalscale=18533.62 is significantly improved compared that of original scale SMR model (MSE=155938.9), which implies anapparent enhancement in accuracy.
  11. 11. VII. Forecasting Comparing all the models from parts II to VI, we conclude that Multiplicative Winter’s Method is the best model in this case, in that it has the MSD=11151.9, R- square=99.72%, autocorrelation fails to violate independence. Although Holt’s two- parameter model has slight better MSD=8798.29 and R square=99.69%, it cancels the noise caused by seasonality. All above indicates Multiplicative Winter’s Method has the highest degree of model adequacy, and forecast accuracy. Moreover, Multiplicative Winter’s Method applies three smooth constant, which allow strongest adaptability to capture the observation. In terms of interpretability, our gut feeling in Data Understanding concluded that Multiplicative Holt-Winters Method may be a strongly suitable model, because sales seems to maintain a linear trend with a consistent multiplicative seasonal pattern in an increasing variation--- sales peaks at Q4 every year through initial peak at 3,931 in 1993 Q4 to 10,786 in 2001 Q4. Our final conclusion exactly resonates with our intuition.