# Mean functions for functional time series

### Description

Computes mean of functional time series at each variable.

### Usage

1 2 3 |

### Arguments

`x` |
An object of class |

`method` |
Method for computing the mean function. |

`na.rm` |
A logical value indicating whether NA values should be stripped before the computation proceeds. |

`alpha` |
Tuning parameter when |

`beta` |
Trimming percentage, by default it is 0.25, when |

`weight` |
Hard thresholding or soft thresholding. |

`...` |
Other arguments. |

### Details

If `method = "coordinate"`

, it computes the coordinate-wise functional mean.

If `method = "FM"`

, it computes the mean of trimmed functional data ordered by the functional depth of Fraiman and Muniz (2001).

If `method = "mode"`

, it computes the mean of trimmed functional data ordered by *h*-modal functional depth.

If `method = "RP"`

, it computes the mean of trimmed functional data ordered by random projection depth.

If `method = "RPD"`

, it computes the mean of trimmed functional data ordered by random projection derivative depth.

If `method = "radius"`

, it computes the mean of trimmed functional data ordered by the notion of alpha-radius.

### Value

A list containing `x`

= variables and `y`

= mean rates.

### Author(s)

Rob J Hyndman, Han Lin Shang

### References

O. Hossjer and C. Croux (1995) "Generalized univariate signed rank statistics for testing and estimating a multivariate location parameter", *Journal of Nonparametric Statistics*, **4**(3), 293-308.

A. Cuevas and M. Febrero and R. Fraiman (2006) "On the use of bootstrap for estimating functions with functional data", *Computational Statistics \& Data Analysis*, **51**(2), 1063-1074.

A. Cuevas and M. Febrero and R. Fraiman (2007), "Robust estimation and classification for functional data via projection-based depth notions", *Computational Statistics*, **22**(3), 481-496.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2007) "A functional analysis of NOx levels: location and scale estimation and outlier detection", *Computational Statistics*, **22**(3), 411-427.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2008) "Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels", *Environmetrics*, **19**(4), 331-345.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2010) "Measures of influence for the functional linear model with scalar response", *Journal of Multivariate Analysis*, **101**(2), 327-339.

J. A. Cuesta-Albertos and A. Nieto-Reyes (2010) "Functional classification and the random Tukey depth. Practical issues", Combining Soft Computing and Statistical Methods in Data Analysis, Advances in Intelligent and Soft Computing, Volume 77, 123-130.

D. Gervini (2012) "Outlier detection and trimmed estimation in general functional spaces", *Statistica Sinica*, **22**(4), 1639-1660.

### See Also

`median.fts`

, `var.fts`

, `sd.fts`

, `quantile.fts`

### Examples

1 2 3 4 5 6 7 8 | ```
# Calculate the mean function by the different depth measures.
mean(x = ElNino, method = "coordinate")
mean(x = ElNino, method = "FM")
mean(x = ElNino, method = "mode")
mean(x = ElNino, method = "RP")
mean(x = ElNino, method = "RPD")
mean(x = ElNino, method = "radius", alpha = 0.5, beta = 0.25, weight = "hard")
mean(x = ElNino, method = "radius", alpha = 0.5, beta = 0.25, weight = "soft")
``` |