Horta_Ziegelmann_FPCA: Dynamic functional principal component analysis for density...

In ftsa: Functional Time Series Analysis

Dynamic functional principal component analysis for density forecasting

Description

Implementation of a dynamic functional principal component analysis to forecast densities.

Usage

Horta_Ziegelmann_FPCA(data, gridpoints, h_scale = 1, p = 5, m = 5001, 
	kernel = c("gaussian", "epanechnikov"), band_choice = c("Silverman", "DPI"), 
	VAR_type = "both", lag_maximum = 6, no_boot = 1000, alpha_val = 0.1, 
	ncomp_select = "TRUE", D_val = 10)

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
p	Number of backward parameters
m	Number of grid points
kernel	Type of kernel function
band_choice	Selection of optimal bandwidth
VAR_type	Type of vector autoregressive process
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
ncomp_select	A tuning parameter in the super_fun function
D_val	A tuning parameter in the super_fun function

Details

1) Compute a kernel covariance function 2) Via eigen-decomposition, a density can be decomposed into a set of functional principal components and their associated scores 3) Fit a vector autoregressive model to the scores with the order selected by Akaike information criterion 4) By multiplying the estimated functional principal components with the forecast scores, obtain forecast densities 5) Since forecast densities may neither be non-negative nor sum to one, normalize the forecast densities accordingly

Value

Yhat.fix_den	Forecast density
u	Grid points
du	Distance between two successive grid points
Ybar_est	Mean of density functions
psihat_est	Estimated functional principal components
etahat_est	Estimated principal component scores
etahat_pred_val	Forecast principal component scores
selected_d0	Selected number of components
selected_d0_pvalues	p-values associated with the selected functional principal components
thetahat_val	Estimated eigenvalues

Author(s)

Han Lin Shang

References

Horta, E. and Ziegelmann, F. (2018) ‘Dynamics of financial returns densities: A functional approach applied to the Bovespa intraday index’, International Journal of Forecasting, 34, 75-88.

Bathia, N., Yao, Q. and Ziegelmann, F. (2010) ‘Identifying the finite dimensionality of curve time series’, The Annals of Statistics, 38, 3353-3386.

See Also

CoDa_FPCA, LQDT_FPCA, skew_t_fun

Examples

## Not run: 
Horta_Ziegelmann_FPCA(data = DJI_return, kernel = "epanechnikov", 
				band_choice = "DPI", ncomp_select = "FALSE")

## End(Not run)

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