qspec.lwqs {qfa}

Lag-Window-Quantile-Smoothing (LWQS) Estimator of Quantile Spectrum

Description

This function computes lag-window-quantile-smoothing (LWQS) estimate of quantile spectrum/cross-spectrum from time series or quantile autocovariance function (QACF).

Usage

qspec.lwqs(
  y,
  tau,
  y.qacf = NULL,
  M = NULL,
  method = c("gamm", "sp"),
  spar = "GCV",
  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 in (0,1)

y.qacf

matrix or array of pre-calculated QACF (default = NULL: compute from y and tau); if y.qacf is supplied, y and tau can be left unspecified

M

bandwidth parameter of lag window (default = NULL: quantile periodogram)

method

smoothing method: "gamm" for mgcv::gamm() (default), "sp" for stats::smooth.spline()

spar

smoothing parameter in smooth.spline() if method = "sp" (default = "GCV")

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:

spec

matrix or array of quantile spectrum/cross-spectrum

spec.lw

matrix or array of quantile spectrum/cross-spectrum without quantile smoothing

lw

lag-window sequence

qacf

matrix or array of quantile autocovariance function if y.qacf = NULL

Examples

y1 <- stats::arima.sim(list(order=c(1,0,0), ar=0.5), n=64)
y2 <- stats::arima.sim(list(order=c(1,0,0), ar=-0.5), n=64)
tau <- seq(0.1,0.9,0.05)
n <- length(y1)
ff <- c(0:(n-1))/n
sel.f <- which(ff > 0 & ff < 0.5)
y.qper.lwqs <- qspec.lwqs(cbind(y1,y2),tau,M=5,method="sp",spar=0.9)$spec
qfa.plot(ff[sel.f],tau,Re(y.qper.lwqs[1,1,sel.f,]))