dcs {DCSmooth}

Nonparametric Double Conditional Smoothing for 2D Surfaces

Description

dcs provides a double conditional nonparametric smoothing of the expectation surface of a functional time series or a random field on a lattice. Bandwidth selection is done via an iterative plug-in method.

Usage

dcs(Y, dcs_options = set.options(), h = "auto", parallel = FALSE, ...)

Arguments

Y

A numeric matrix that contains the observations of the random field or functional time-series.

dcs_options

An object of class "dcs_options", specifying the parameters for the smoothing and bandwidth selection procedure.

h

Bandwidth for smoothing the observations in Y. Can be a two-valued numerical vector with bandwidths in row- and column-direction. If the value is "auto" (the default), bandwidth selection will be carried out by the iterative plug-in algorithm.

parallel

A logical value indicating if parallel computing should be used for faster computation. Default value is parallel = FALSE. Parallelization seems to be efficient at above 400,000 observations.

...

Additional arguments passed to dcs. Currently supported are numerical vectors X and/or T containing the exogenous covariates with respect to the rows and columns.

Value

dcs returns an object of class "dcs", including

Y	matrix of original observations.
X, T	vectors of covariates over rows (X) and columns (T).
M	resulting matrix of smoothed values.
R	matrix of residuals of estimation, Y - M.
h	optimized or given bandwidths.
c_f	estimated variance coefficient.
var_est	estimated variance model. If the variance function is modeled by an SARMA/SFARIMA, var_est is an object of class "sarma"/ "sfarima".
dcs_options	an object of class cds_options containing the initial options of the dcs procedure.
iterations	number of iterations of the IPI-procedure.
time_used	time spend searching for optimal bandwidths (not overall runtime of the function).

Details

See the vignette for a more detailed description of the function.

References

Schäfer, B. and Feng, Y. (2021). Fast Computation and Bandwidth Selection Algorithms for Smoothing Functional Time Series. Working Papers CIE 143, Paderborn University.

See Also

set.options

Examples

# See vignette("DCSmooth") for examples and explanation

y <- y.norm1 + matrix(rnorm(101^2), nrow = 101, ncol = 101)
dcs(y)