Description Usage Arguments Details Value References Examples

`multi_lag_test`

Computes the multi-lag hypothesis test over a range of user-specified lags.

1 2 3 4 5 6 7 8 9 10 |

`f_data` |
the functional data matrix with observed functions in the columns |

`lag` |
Positive integer value. The lag to use to compute the single lag test statistic |

`M` |
Positive integer value. Number of Monte-Carlo simulation for Welch-Satterthwaite approximation. |

`low_disc` |
A Boolean value, FALSE by default. If given TRUE, uses low-discrepancy sampling in the Monte-Carlo method. Note, low-discrepancy sampling will yield deterministic results. Requires the 'fOptions' package. |

`iid` |
A Boolean value, FALSE by default. If given TRUE, the hypothesis test will use a strong-white noise assumption (instead of a weak-white noise assumption). |

`alpha` |
Numeric value between 0 and 1 specifying the significance level to be used in the specified hypothesis test. The default value is 0.05. Note, the significance value is only ever used to compute the 1-alpha quantile of the limiting distribution of the specified test's test statistic. |

`suppress_raw_output` |
Boolean value, FALSE by default. If TRUE, the function will not return the list containing the p-value, quantile, and statistic. |

`suppress_print_output` |
Boolean value, FALSE by default. If TRUE, the function will not print any output to the console. |

The "multi-lag" portmanteau test is also based on the sample autocovariance function computed from the functional data. This test assesses the cumulative significance of lagged autocovariance operators, up to a user-selected maximum lag K. More specifically, it tests the null hypothesis that the first K lag-h autocovariance operators (h going from 1 to K) is equal to 0. This test is designed for stationary functional time-series, and is valid under conditional heteroscedasticity conditions.

If suppress_raw_output = FALSE, a list containing the test statistic, the 1-alpha quantile of the limiting distribution, and the p-value computed from the specified hypothesis test. Also prints output containing a short description of the test, the p-value, and additional information about the test if suppress_print_output = FALSE.

[1] Kokoszka P., & Rice G., & Shang H.L. (2017). Inference for the autocovariance of a functional time series under conditional heteroscedasticity. Journal of Multivariate Analysis, 162, 32-50.

1 2 3 | ```
b <- brown_motion(150, 50)
multi_lag_test(b, lag = 5)
multi_lag_test(b, lag = 10, M = 50)
``` |

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