ftsa (version 6.4)

CoDa_BayesNW: Compositional data analytic approach and nonparametric function-on-function regression for forecasting density

Description

Log-ratio transformation from constrained space to unconstrained space, where a standard nonparametric function-on-function regression can be applied.

Usage

CoDa_BayesNW(data, normalization, m = 5001, 
	band_choice = c("Silverman", "DPI"), 
	kernel = c("gaussian", "epanechnikov"))

Value

Out-of-sample density forecasts

Arguments

data

Densities or raw data matrix of dimension N by p, where N denotes sample size and p denotes dimensionality

normalization

If a standardization should be performed?

m

Grid points within the data range

band_choice

Selection of optimal bandwidth

kernel

Type of kernel function

Author

Han Lin Shang

Details

1) Compute the geometric mean function 2) Apply the centered log-ratio transformation 3) Apply a nonparametric function-on-function regression to the transformed data 4) Transform forecasts back to the compositional data 5) Add back the geometric means, to obtain the forecasts of the density function

References

Egozcue, J. J., Diaz-Barrero, J. L. and Pawlowsky-Glahn, V. (2006) `Hilbert space of probability density functions based on Aitchison geometry', Acta Mathematica Sinica, 22, 1175-1182.

Ferraty, F. and Shang, H. L. (2021) `Nonparametric density-on-density regression', working paper.

See Also

CoDa_FPCA

Examples

if (FALSE) {
CoDa_BayesNW(data = DJI_return, normalization = "TRUE", 
		band_choice = "DPI", kernel = "epanechnikov")
}