Select the method or formula of your choice.

The graphs for the autocorrelation function (ACF) of the ARIMA residuals include lines that represent the significance limits. Values that extend beyond the significance limits are statistically significant at approximately *α* = 0.05, and show evidence that the autocorrelation does not equal zero.

Term | Description |
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k | lag; k = 1, 2,... |

x _{t} | value of x at row t |

mean of x | |

n | number of observations in the series |

Term | Description |
---|---|

k | lag; k = 1, 2, ... |

n | number of observations in the series |

autocorrelation of lag m |

Term | Description |
---|---|

autocorrelation at lag k; k = 1, 2, ... | |

standard error of the autocorrelation at lag k |

Upper limit at lag *k* = *t* _{ n−1; 0.975} × SE(*r _{k} *)

Lower limit at lag *k* = *t* _{ n−1; 0.025} × SE(*r _{k} *)

Term | Description |
---|---|

SE(r) _{k} | standard error of the autocorrelation at lag k |

t _{ n-1; 0.975} | 97.5^{th} percentile of the t distribution with n – 1 degrees of freedom |

t _{ n-1; 0.025} | 2.5^{th} percentile of the t distribution with n – 1 degrees of freedom |

Term | Description |
---|---|

n | number of observations in a series |

estimated autocorrelation at lag m; m = 1, 2, ..., k | |

k | lag; k = 1, 2, ... |