qspec.ar: Autoregression (AR) Estimator of Quantile Spectrum

In qfa: Quantile-Frequency Analysis (QFA) of Time Series

Autoregression (AR) Estimator of Quantile Spectrum

Description

This function computes autoregression (AR) estimate of quantile spectrum from time series or quantile series (QSER).

Usage

qspec.ar(
  y,
  tau,
  y.qser = NULL,
  p = NULL,
  order.max = NULL,
  freq = NULL,
  method = c("none", "gamm", "sp"),
  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.qser	matrix or array of pre-calculated QSER (default = NULL: compute from y and tau);
p	order of AR model (default = NULL: automatically selected by AIC)
order.max	maximum order for AIC if p = NULL (default = NULL: determined by stats::ar())
freq	sequence of frequencies in [0,1) (default = NULL: all Fourier frequencies)
method	quantile smoothing method: "gamm" for mgcv::gamm(), "sp" for stats::smooth.spline(), or "none" (default) if y.qser is supplied, y and tau can be left unspecified
n.cores	number of cores for parallel computing of QDFT if y.qser = NULL (default = 1)
cl	pre-existing cluster for repeated parallel computing of QDFT (default = NULL)

Value

a list with the following elements:

spec	matrix or array of AR quantile spectrum
freq	sequence of frequencies
fit	object of AR model
qser	matrix or array of quantile series if y.qser = 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)
y <- cbind(y1,y2)
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.qspec.ar <- qspec.ar(y,tau,p=1)$spec
qfa.plot(ff[sel.f],tau,Re(y.qspec.ar[1,1,sel.f,]))
y.qser <- qcser(y1,tau)
y.qspec.ar <- qspec.ar(y.qser=y.qser,p=1)$spec
qfa.plot(ff[sel.f],tau,Re(y.qspec.ar[sel.f,]))
y.qspec.arqs <- qspec.ar(y.qser=y.qser,p=1,method="sp")$spec
qfa.plot(ff[sel.f],tau,Re(y.qspec.arqs[sel.f,]))

qfa documentation built on April 11, 2025, 5:49 p.m.