qser2sar: Spline Autoregression (SAR) Model of Quantile Series

Description

This function fits spline autoregression (SAR) model to quantile series (QSER).

Usage

qser2sar(
  y.qser,
  tau0,
  tau = tau0,
  p = NULL,
  order.max = NULL,
  spar = NULL,
  method = c("GCV", "AIC", "BIC"),
  type = c(1, 2),
  weights = rep(1, length(tau0)),
  interval = c(-1.5, 1.5)
)

Value

a list with the following elements:

A: matrix or array of SAR coefficients
V: vector or matrix of SAR residual covariance
p: order of SAR model
spar: penalty parameter
n: length of time series
tau: quantile levels for evaluation
tau0: quantile levels for fitting
weights: weights in penalty function
sdm: spline design matrices
fit: object containing details of SAR fit

Arguments

y.qser: matrix or array of pre-calculated QSER at tau0 using, e.g., qser()
tau0: quantile levels used to compute y.qser
tau: quantile levels for evaluation (min(tau0) <= tau <= max(tau0); default = tau0)
p: order of SAR model (default = NULL: automatically selected by AIC)
order.max: maximum order for AIC if p = NULL (default = NULL: determined by stats::ar())
spar: penalty parameter alla stats::smooth.spline() (default = NULL: automatically selected)
method: criterion for penalty parameter selection: "GCV" (default), "AIC", or "BIC"
type: type of quantile smoothing for residual variance: 1 = direct (default) or 2 = square root
weights: sequence of weights (default = rep(1,length(tau0)))
interval: interval for spar optimization (default = c(-1.5,1.5))