LQDT_FPCA: Log quantile density transform

In ftsa: Functional Time Series Analysis

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 Sept. 11, 2023, 5:09 p.m.