Operations

Problem 1

In performing a time series analysis based on the data provided from January 1990 to December 2007, the following models are used (See excel file)

After creating the models shown above, their accuracy is summarized in the following table (1990 – 2007):

Forecast Method | MAD | MAPD | Cumulative Error | Ranking |

Adjusted Exponential #2 | 0.035708 | 0.004526 | 0.350044868 | 1 |

3 Month Weighted Moving Average | 0.03757 | 0.003907 | 2.5862896 | 2 |

Adjusted Exponential #1 | 0.042921 | 0.004526 | 3.907060336 | 3 |

3 Month Simple Moving Average | 0.044438 | 0.004681 | 3.453417667 | 4 |

Exponential Smoothing | 0.052199 | 0.005505 | 5.717595694 | 5 |

Linear Trend | 0.106212 | 0.011201 | 1.07292E-12 | 6 |

Regression | 0.106212 | 0.011201 | 1.07292E-12 | 7 |

Mean absolute deviation, or MAD, was the chosen measure to rank the models from best to worst and this is consistent with the other years followed.

The values for alpha and beta were chosen to be 0.8 because the closer the values are to 1.0, the more weight is distributed to the recent trend data. The data values relate to the Canadian economy and the users of this data tend to express concerns towards the recent data since it is correlated to their investments, the financial performance of the country, etc.

The seasonality test was conducted and the following graph suggests that the forecast has to be adjusted with the seasonal index.

The seasonal index is calculated (see Excel) and is applied to the model of choice – Adjusted Exponential of choice (α = 0.8, β = 0.8): (See excel)

After creating the models shown above, their accuracy is summarized in the following table (2008 – 2009):

Forecast Method | MAD | MAPD | Cumulative Error | Ranking |

Adjusted Exponential #2 | 0.053256594 | 0.005188794 | 0.015300166 | 1 |

3 Month Weighted Moving Average | 0.065615783 | 0.006392951 | -0.1692494 | 2 |

Adjusted Exponential #1 | 0.077669746 | 0.007567369 | -0.328420038 | 3 |...