Each model receives as input the past observations of the time series and the estimation of the next mode. The independence of each model means that each model may be defined arbitrarily (for example, one model may be defined using ANN, another using Holt–Winters while the others using ARIMA). Also, each model defines the number of previous observations (that is the structure) to use in the prediction. In our case, each model in the bank of models (BM) is defined by a three-layer fully connected ANN while the architecture and the training of the net is performed by GAs. The inputs and the outputs of each model are defined in Table 1.

Table 1

. | Input . | Output . |
---|---|---|

Model 1 | {y_{t}_{−k1}, y_{t}_{−k1+1}, y_{t}_{−k1+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+1} |

Model 2 | {y_{t}_{−k2}, y_{t}_{−k2+1}, y_{t}_{−k2+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+2} |

Model 3 | {y_{t}_{−k3}, y_{t}_{−k3+1}, y_{t}_{−k3+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+3} |

… | ||

Model 23 | {y_{t}_{−k23}, y_{t}_{−k23+1}, y_{t−k}_{23+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+23} |

Model 24 | {y_{t}_{−k24}, y_{t}_{−k24+1}, y_{t}_{−k24+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+24} |

. | Input . | Output . |
---|---|---|

Model 1 | {y_{t}_{−k1}, y_{t}_{−k1+1}, y_{t}_{−k1+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+1} |

Model 2 | {y_{t}_{−k2}, y_{t}_{−k2+1}, y_{t}_{−k2+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+2} |

Model 3 | {y_{t}_{−k3}, y_{t}_{−k3+1}, y_{t}_{−k3+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+3} |

… | ||

Model 23 | {y_{t}_{−k23}, y_{t}_{−k23+1}, y_{t−k}_{23+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+23} |

Model 24 | {y_{t}_{−k24}, y_{t}_{−k24+1}, y_{t}_{−k24+2}, …, y_{t}_{−1}, y, _{t}M} _{i} | y_{t}_{+24} |

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