LQDT_FPCA: Log quantile density transform

View source: R/LQDT_FPCA.R

LQDT_FPCAR Documentation

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)

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

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.

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

Author(s)

Han Lin Shang

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

## Not run: 
LQDT_FPCA(data = DJI_return, band_choice = "DPI", kernel = "epanechnikov", 
			forecasting_method = "uni", fmethod = "ets")

## End(Not run)		

ftsa documentation built on May 29, 2024, 2:47 a.m.