Parameter Determination of Dynamic Equation Model

Dynamic equation (3.4) in the integral form of the Eq. (3.5) has three parameters K, X and b. And to apply dynamic equation (3.4) to customer demand forecasts, we must fix the values of these parameters firstly. It is recommended in our study that the 

In the Eq. (3.5), if we set KX = a, the Eq. (3.5) degenerates into classic Logistic model (3.1). For Logistic model (3.1), the concept of reciprocal summation method can be explained that we can divide the given data (t , = 1,2. A into three 

Take logarithm on both sides and get InDa — InDi = ar, thus 

According to properties of the function Y = Y(t), Eq. (3.5) has properties of common growth curves. Hence, we attempt to use value K obtained by Gompertz model approximation as the value K for Eq. (3.4). In order to get Gompertz model parameters, methods like Sanwa method, reciprocal summation method can be used to solve the needed parameters. The introduction of Sanwa method is that the entire time series is divided into intervals which are equal to each other, and the logarithms sum of three observation values is used to calculate the parameters. 

A defined time series To, Yi. T i, Y ,..Y2 -i,Y2n, , Tsn-i (if the number of data is not divisible by 3, we can increase or decrease the individual data to make it just as a multiple of 3. It is important that the time series can also be started from t = 1) have been evenly divided into three sections, and the logarithms sum of three observation values are as follows  

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