WILMORE PAPER COMPANY

Advertising Budget Model

Time Series Analysis by Burcu Arikan, Spring 2008

Verification

Verification of best fit for the time series models is based on the optimal combination of four statistical measures: Residual Sum of Squares (RSS), the Durbin-Watson (D-W) statistic, t-ratios of unstandardized coefficients, and the calculated Average Percentage Error (APE).

The Durbin-Watson statistic measures autocorrelation in the successive sample to determine whether sequential measures are correlated to each other, a condition which theoretically weakens the predictability of the model. In cases involving historical advertising data, it is understood that advertising expenditures generate consumer impressions which carry over to subsequent time periods. Autocorrelation weakens the predictability and validity of these models, so it is best to use a model without autocorrelation. The Logistic model yields the highest Durbin-Watson statistic (1.077), reflecting the lowest level of autocorrelation among the tested models.

Residual Sum of Squares (RSS) should be low to reflect goodness of fit. The Durbin-Watson statistic measures autocorrelation in the successive sample to determine whether sequential measures are correlated to each other, a condition which theoretically weakens the predictability of the model. Of course, in this case, they are, so we expect to find high autocorrelation in each of our models because of the nature of the data set. In order for the model to be useful, it must be generalizeable to the general population, so the regression coefficient of the selected model must be statistically significant. The best-fit model should be the one in which each statistic is optimized. Comparison of RSS values yields lowest values for the Logistic, and Modified Exponential models.

In order for the model to be useful, it must be generalizeable to the general population, so the regression coefficient of the selected model must be statistically significant. Most of the models tested have statistically significant (t < .001) unstandardized correlation coefficients, except the a parameters of the Linear model and the Power model.

Referring to Average Percentage Error (APE) shows that the three models with the lowest percentage error are Logistic (1.74%), LB (1.16%) and Modified Exponential (1.93%) Models.

All factors considered, the Logistic Function model shows the least problematic set of statistics combined with acceptable APE, and is the model that will be used in this exercise to predict future sales, Spring Quarter 2008 for the Wilmore Paper Company.

Average percentage error is calculated for each predictive model to test validity using the equation APE = Actual Sales - Predicted Sales/Actual Sales. See the Validation page of this site for more discussion on the "acid test." Logistic model yields the best statistical result (APE = 1.74%).