WILMORE PAPER COMPANY
Advertising Budget Model
Time Series Analysis by Burcu Arikan, Spring 2008
| Introduction | Specification | Estimation | Verification | Validation | Budget |
Estimation
For the estimation step, nine Current Effects functions were applied to the data to determine the best fit.Parameters of the nine current effects functional models were estimated by conducting linear regression analysis. Variables (i.e., advertising expenditure or sales) were transformed as needed to fit the model equations. For each functional model, unstandardized coefficients and their t ratios, RSS, Durbin-Watson statistics and APE are reported to assess the overall model fit. Regression analysis used sequential annual data from Fall 2000- Winter 2008 to produce response function parameters. Data for Summer 2007, Fall 2007 and Winter 2008 were set aside for model validation. The results of regression analyses are shown in Table 1.
TABLE 2. LINEAR REGRESSION RESULTS FOR NINE CURRENT EFFECTS MODELS, AND AVERAGE PERCENTAGE ERROR
| Function | Unstandardized Coefficients | t | Durbin-Watson | RSS | APE | |
| Linear | a |
104.206 |
.679 |
.403** | 3.71E+12 | 7.3% |
| b | 1.370 | 19.836* | ||||
| Logistic *** | a |
-2.699 |
-29.733* |
1.077** | 3.46E+12 | 1.74 % |
| b | .002 | 45.525* | ||||
| LB (Lower Bound) *** | a b |
3.375 -.002 |
24.524* -33.593* |
.639** | 7.54E+13 | 1.16 % |
| Modified Exponential *** | a b |
.691 -.001 |
6.498* -24.821* |
.410** | 2.87E+13 | 1.93 % |
Power |
a b |
.731 .948 |
1.843 17.627* |
.680** | 3.66E+13 | 13.43 % |
| Gompertz*** | a b |
1.545 -.001 |
18.797* -39.721* |
.890** | 9.06E+13 | 7.33% |
| Logarithmic | a b |
-9850.3 1720.6 |
-8.859* 11.419* |
.411** | 9.98E+13 | 5.1 % |
| Square Root | a b |
-1765.352 108.094 |
-7.399* 19.989* |
.591** | 3.65E+12 | 7.67% |
| Quadratic | a b1 b2 |
-509.4 2.256 .000 |
-2.601* 9.871* -3.993* |
.781** | 6.14E+13 | 78.16% |
*p< .05, **DW<1.5 (Significant auto-correlation), sample size=30
***Upper Bound=4700 and Lower Bound=300 (if LB applies).