Algorithm 1.

The GA algorithm to find the optimal $\gamma ,\beta ,\alpha$.

Set the objective function and the maximum iteration number Input: The original parameters $\beta ,\gamma ,\alpha$, original data and the number of modelling data Output: The best $\beta ,\gamma ,\alpha$ for $\beta \in \left(-1,+\infty \right)$do Substitute $\beta ,\gamma ,\alpha$ to $\widehat{P}={\left(B^{T}B\right)}^{-1}{B}^{T}Y$ and obtain parameters $P={\left(a,b,c\right)}^T$ Substitute parameters to discrete equation Eq. (14) and compute the simulation value to obtain ${\widehat{X}}^{\left(1\right)}\left(k\right)$ Compute ${\widehat{X}}^{\left(0\right)}\left(k\right)$ in Eq. (16) Compute APE and MAPE in Table 2. End Update the minimum MAPE value Return the best $\beta ,\gamma ,\alpha$ by the GA algorithm.