tsqr.fit: Trigonometric Spline Quantile Regression (TSQR) of Time...

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

Trigonometric Spline Quantile Regression (TSQR) of Time Series

Description

This function computes trigonometric spline quantile regression (TSQR) for univariate time series at a single frequency using sqr.fit(), sqr1.fit(), or sqr3.fit().

Usage

tsqr.fit(
  y,
  f0,
  tau,
  tau0 = tau,
  spar = 1,
  w = rep(1, length(tau0)),
  mthreads = FALSE,
  prepared = TRUE,
  method = c("sqr", "sqr1", "sqr3"),
  ztol = NULL,
  solver = NULL,
  all.knots = FALSE,
  control = list()
)

Arguments

y	time series
f0	frequency in [0,1)
tau	sequence of quantile levels for evaluation
tau0	sequence of quantile levels for fitting (min(tau0) <= tau <= max(tau0); default = tau)
spar	smoothing parameter (default = 1)
w	weight sequence in penalty (default = rep(1,length(tau0)))
mthreads	if FALSE (default), set RhpcBLASctl::blas_set_num_threads(1)
prepared	if TRUE, intercept is removed and coef of cosine is doubled when f0 = 0.5
method	'sqr' (default), "sqr1", or 'sqr3'
ztol	a zero tolerance paramete 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)
all.knots	TRUE or FALSE (default), as in stats::smooth.spline()
control	list of control parameters for QP solvers 'piqp' and 'osqp'

Value

object of sqr.fit(), sqr1.fit(), or sqr3.fit()

Examples

y <- stats::arima.sim(list(order=c(1,0,0), ar=0.5), n=64)
tau <- seq(0.1,0.9,0.05)
tau0 <- seq(0.1,0.9,0.2)
fit <- tqr.fit(y,f0=0.1,tau=tau)
fit.sqr1 <- tsqr.fit(y,f0=0.1,tau=tau,tau0=tau0,spar=0.2,method='sqr1')
fit.sqr3 <- tsqr.fit(y,f0=0.1,tau=tau,tau0=tau0,spar=1,method='sqr3')
plot(tau,fit$coef[1,],type='p',xlab='QUANTILE LEVEL',ylab='TQR COEF')
lines(tau,fit.sqr1$coef[1,])
lines(tau,fit.sqr3$coef[1,],col=2)

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