SETS:
! Estimate the Bass model for new product sales(BASSMODEL);
! Keywords: forecasting, Bass model, new product diffusion,
  Logistic curve;
! Bass(1969) introduced a model for predicting 
  first purchases of a new product. 
  The following three parameters specify the model:
     M  = estimate of the market size,  that is, 
          the total number of customers that will 
          eventually buy the product. 
          For simplicity,  we assume that the product is a
          durable good,  so that a customer will
          purchase it at most once.
      p = probability that a candidate customer in a given
          period will purchase the product just by chance,
          without any influence from existing customers.
          These folk are called the innovators.
      q = rate at which a candidate customer is induced 
          to purchase the product because of interaction with
          existing customers.  The greater the number of 
          existing customers,  the greater the inducement.
          These folk are the followers;
 ! If p = 0, then the Bass model approximates a discrete time
   version of the logistic model for total cumulative sales.
   If q = 0, then the Bass model approximates a discrete time
   version of the exponential cdf for total cumulative sales;

 PERIOD: SALES, CUM, ERROR, FORECAST;
ENDSETS
DATA:
! Weekly sales data for the movie: "The Doctor", see
   Lilien & Rangaswamy;
 PERIOD = 1..12;
 SALES = 0.1  3.0  5.2  7.0  5.25  4.9
         3.0  2.4  1.9  1.3  0.8   0.6;
! No. of observations for "training" model;
  TRAINON = 9;
! Upper and lower limits on parameters;
    ULP = 1.0; ULQ = 1.0; ULM = 9999;
    LLP = 0.0; LLQ = 0.0; LLM = 0.0;
ENDDATA
! Errors can be negative or positive;
@FOR( PERIOD( T):
   @FREE( ERROR( T));
   @FREE( FORECAST(T));
 );

FORECAST( 1) = P * M;
CUM( 1) = SALES( 1);
ERROR( 1) = FORECAST(1) - SALES( 1);

@FOR( PERIOD( T)| T #GT# 1:
! The fundamental forecast formula;
   FORECAST( T) = 
          ( P + Q * CUM( T - 1)/ M)*( M - CUM( T - 1));
   CUM( T) = SALES( T) + CUM( T - 1);
   ERROR( T) = FORECAST( T) - SALES( T);
 ); 

MIN = ! Min sum of squared errors on training sample;
 @SUM( PERIOD( T)| T #LE# TRAINON: ERROR( T) * ERROR( T));
! Enforce bounds on parameters;

 @BND( LLP, P, ULP); @BND( LLQ, Q, ULQ); @BND( LLM, M, ULM);