Forecasting ModelSBass Diffusion Model
Building a Bass Diffusion Model to forecast the adoption of an ‘innovation’ or new product into a market. The model attempts to predict how many customers will eventually adopt the new product and when they will adopt which acts as a guide for methodically deploying resources into marketing the ‘innovation.’
where M is market size
p is coefficient of innovation (or coefficient of external influence)
q is coefficient of imitation (or coefficient of internal influence)
p < q
p > q
Revenue Forecasting
Using Apple’s historical revenue data, I built a model to predict revenues for each quarter. First, a two quarter moving average was calculated as the first forecast.
I then found a smoothing parameter (alpha) by using Excel’s solver to minimize the sum of squared errors (SSE). The smoothed forecast was found using the equation below.
Holt-Winters Model
For this model, I built a model to calculated a one-step forecast of the Apple revenue data using a dynamic level, trend, and seasonality variables.
First, I initialized the model using the first eight observations to find the trend and seasonality coefficients of each quarter which were dummy coded.
Then, I found the initial value for level but subtracting that quarter’s seasonality coefficient.
Then, I was able to forecast from the ninth observation. The following was then calculated using smoothing parameters which were found using minimizing SSE with solver.
