Description Usage Arguments Details Value Author(s) References See Also Examples

The coefficients from the fitted object are forecasted using a multivariate time-series forecasting method. The forecast coefficients are then multiplied by the functional principal components to obtain a forecast curve.

1 2 | ```
farforecast(object, h = 10, var_type = "const", Dmax_value, Pmax_value,
level = 80, PI = FALSE)
``` |

`object` |
An object of |

`h` |
Forecast horizon. |

`var_type` |
Type of multivariate time series forecasting method; see |

`Dmax_value` |
Maximum number of components considered. |

`Pmax_value` |
Maximum order of VAR model considered. |

`level` |
Nominal coverage probability of prediction error bands. |

`PI` |
When |

1. Decompose the smooth curves via a functional principal component analysis (FPCA).

2. Fit a multivariate time-series model to the principal component score matrix.

3. Forecast the principal component scores using the fitted multivariate time-series models. The order of VAR is selected optimally via an information criterion.

4. Multiply the forecast principal component scores by estimated principal components to obtain forecasts of *f_{n+h}(x)*.

5. Prediction intervals are constructed by taking quantiles of the one-step-ahead forecast errors.

`point_fore` |
Point forecast |

`order_select` |
Selected VAR order and number of components |

`PI_lb` |
Lower bound of a prediction interval |

`PI_ub` |
Upper bound of a prediction interval |

Han Lin Shang

A. Aue, D. D. Norinho and S. Hormann (2015) "On the prediction of stationary functional time series", *Journal of the American Statistical Association*, **110**(509), 378-392.

J. Klepsch, C. Kl\"uppelberg and T. Wei (2017) "Prediction of functional ARMA processes with an application to traffic data", *Econometrics and Statistics*, **1**, 128-149.

1 2 3 | ```
sqrt_pm10 = sqrt(pm_10_GR$y)
multi_forecast_sqrt_pm10 = farforecast(object = fts(seq(0, 23.5, by = 0.5), sqrt_pm10),
h = 1, Dmax_value = 5, Pmax_value = 3)
``` |

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