sqdft: Spline Quantile Discrete Fourier Transform (SQDFT) of Time...

In qfa: Quantile-Frequency Analysis (QFA) of Time Series and Spline Quantile Regression (SQR)

Spline Quantile Discrete Fourier Transform (SQDFT) of Time Series

Description

This function computes spline quantile discrete Fourier transform (SQDFT) for univariate or multivariate time series through trigonometric spline quantile regression.

Usage

sqdft(
  y,
  tau,
  tau0 = tau,
  spar = NULL,
  w = rep(1, length(tau0)),
  criterion = c("AIC", "BIC", "GIC"),
  method = c("sqr", "sqr1", "sqr3"),
  ztol = NULL,
  solver = NULL,
  interval = NULL,
  all.knots = FALSE,
  control = list(),
  n.cores = 1,
  cl = NULL
)

Arguments

y	vector or matrix of time series (if matrix, nrow(y) = length of time series)
tau	sequence of quantile levels for evaluation
tau0	sequence of quantile levels for fitting (min(tau0) <= tau <= max(tau0); default = tau)
spar	smoothing parameter, selected automatically by criterion if spar = NULL or if length(spar) > 1
w	weight sequence in penalty (default = rep(1,length(tau0)))
criterion	criterion for smoothing parameter selection: "AIC" (default), "BIC", or "GIC"
method	'sqr'(default), 'sqr1', or 'sqr3'
ztol	zero-tolerance parameter to determine the model complexity (default = NULL: set internally to 1e-5 for SQR and SQR1 or 1e-4 for SQR3)
solver	'fnb' or 'sfn' for SQR and SQR1; 'piqp' or 'osqp' for SQR3 (default = NULL: set internally to 'fnb' for SQR and SQR1 or 'piqp' for SQR3)
interval	interval for spar optimization (default: c(-1.5,1.5) for SQR and SQR1 or c(0,2.5) for SQR3)
all.knots	TRUE or FALSE (default), as in stats::smooth.spline()
control	list of control parameters for QP solvers 'piqp' and 'osqp' (default = list())
n.cores	number of cores for parallel computing (default = 1)
cl	pre-existing cluster for repeated parallel computing (default = NULL)

Value

A list with the following elements:

coefficients	matrix of regression coefficients
qdft	matrix or array of the spline quantile discrete Fourier transform of y
crit	criteria for smoothing parameter selection: (AIC,BIC,GIC)
nit	maximum number of iterations
spar	optimal value of smoothing parameter

Examples

y <- stats::arima.sim(list(order=c(1,0,0), ar=0.5), n=64)
tau <- seq(0.1,0.9,0.05)
y.sqdft <- sqdft(y,tau,spar=0.2,method="sqr1")$qdft
plot(y.sqdft[,2])

qfa documentation built on March 30, 2026, 5:07 p.m.