ftsa (version 6.4)

LQDT_FPCA: Log quantile density transform

Description

Probability density function, cumulative distribution function and quantile density function are three characterizations of a distribution. Of these three, quantile density function is the least constrained. The only constrain is nonnegative. By taking a log transformation, there is no constrain.

Usage

LQDT_FPCA(data, gridpoints, h_scale = 1, M = 3001, m = 5001, lag_maximum = 4, 
		no_boot = 1000, alpha_val = 0.1, p = 5, 
		band_choice = c("Silverman", "DPI"), 
		kernel = c("gaussian", "epanechnikov"), 
		forecasting_method = c("uni", "multi"), 
		varprop = 0.85, fmethod, VAR_type)

Value

L2Diff

L2 norm difference between reconstructed and actual densities

unifDiff

Uniform Metric excluding missing boundary values (due to boundary cutoff)

density_reconstruct

Reconstructed densities

density_original

Actual densities

dens_fore

Forecast densities

totalMass

Assess loss of mass incurred by boundary cutoff

u

m number of grid points

Arguments

data

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

gridpoints

Grid points

h_scale

Scaling parameter in the kernel density estimator

M

Number of grid points between 0 and 1

m

Number of grid points within the data range

lag_maximum

A tuning parameter in the super_fun function

no_boot

A tuning parameter in the super_fun function

alpha_val

A tuning parameter in the super_fun function

p

Number of backward parameters

band_choice

Selection of optimal bandwidth

kernel

Type of kernel function

forecasting_method

Univariate or multivariate time series forecasting method

varprop

Proportion of variance explained

fmethod

If forecasting_method = "uni", specify a particular forecasting method

VAR_type

If forecasting_method = "multi", specify a particular type of vector autoregressive model

Author

Han Lin Shang

Details

1) Transform the densities f into log quantile densities Y and c specifying the value of the cdf at 0 for the target density f. 2) Compute the predictions for future log quantile density and c value. 3) Transform the forecasts in Step 2) into the predicted density f.

References

Petersen, A. and Muller, H.-G. (2016) `Functional data analysis for density functions by transformation to a Hilbert space', The Annals of Statistics, 44, 183-218.

Jones, M. C. (1992) `Estimating densities, quantiles, quantile densities and density quantiles', Annals of the Institute of Statistical Mathematics, 44, 721-727.

See Also

CoDa_FPCA, Horta_Ziegelmann_FPCA, skew_t_fun

Examples

if (FALSE) {
LQDT_FPCA(data = DJI_return, band_choice = "DPI", kernel = "epanechnikov", 
			forecasting_method = "uni", fmethod = "ets")
}