ftsa (version 4.7)

var.fts: Variance functions for functional time series

Description

Computes variance functions of functional time series at each variable.

Usage

"var"(x, method = c("coordinate", "FM", "mode", "RP", "RPD", "radius"),  trim = 0.25, alpha, weight, ...)

Arguments

x

An object of class fts.

method

Method for computing median.

trim

Percentage of trimming.

alpha

Tuning parameter when method="radius".

weight

Hard thresholding or soft thresholding.

...

Other arguments.

Value

A list containing x = variables and y = variance rates.

Details

If method = "coordinate", it computes coordinate-wise variance.

If method = "FM", it computes the variance of trimmed functional data ordered by the functional depth of Fraiman and Muniz (2001).

If method = "mode", it computes the variance of trimmed functional data ordered by $h$-modal functional depth.

If method = "RP", it computes the variance of trimmed functional data ordered by random projection depth.

If method = "RPD", it computes the variance of trimmed functional data ordered by random projection derivative depth.

If method = "radius", it computes the standard deviation function of trimmed functional data ordered by the notion of alpha-radius.

References

O. Hossjer and C. Croux (1995) "Generalized univariate signed rank statistics for testing and estimating a multivariate location parameter", 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

mean.fts, median.fts, sd.fts, quantile.fts

Examples

# Fraiman-Muniz depth was arguably the oldest functional depth.	
var(x = ElNino, method = "FM")
var(x = ElNino, method = "coordinate")
var(x = ElNino, method = "mode")
var(x = ElNino, method = "RP")
var(x = ElNino, method = "RPD")
var(x = ElNino, method = "radius", alpha = 0.5, weight = "hard")
var(x = ElNino, method = "radius", alpha = 0.5, weight = "soft")