WARp | R Documentation |
this function produces an object of the WARp class which includes WAR(p) model parameter estimates and relevant quantities (see output list)
WARp(quantile, quantile.grid, p)
quantile |
A matrix containing all the sample quantile functions. Columns represent time indices and rows represent evaluation grid. |
quantile.grid |
A numeric vector, the grid over which quantile functions are evaluated. |
p |
A positive integer, the order of the fitted WAR(p) model. |
This function takes in a density time series in the form of the corresponding quantile functions as the main input. If the quantile series is not readily available, a general practice is to estimate density functions from samples, then use dens2quantile
from the fdadensity
package to convert density time series to quantile series.
A WARp
object of:
coef |
estimated AR parameters of the fitted WAR(p) model |
coef.cov |
covariance matrix of |
acvf |
Wasserstein autocovariance function values |
Wass.mean |
Wasserstein mean quantile function |
quantile |
a matrix containing all the sample quantile functions (columns represent time indices and rows represent evaluation grid) |
quantile.grid |
quantile function grid that is utilized in calculation |
order |
a positive integer, the order of the fitted WAR(p) model |
Wasserstein Autoregressive Models for Density Time Series, Chao Zhang, Piotr Kokoszka, Alexander Petersen, 2022
# Simulate a density time series represented in quantile functions # warSimData$sample.ts: A sample TS of quantile functions of length 100, taken from # the simulation experiments in Section 4 of Zhang et al. 2022. # warSimData$quantile.grid: The grid over which quantile functions in sample.ts are evaluated. warSimData <- warSim() p <- 3 dSup <- seq(-2, 2, 0.02) expSup <- seq(-2, 2, 0.1) # Estimation: fit a WAR(3) model WARp_obj <- WARp(warSimData$sample.ts, warSimData$quantile.grid, p) # Forecast: one-step-ahead forecast forecast_1 <- predict(WARp_obj) # dSup and expSup are chosen automatically forecast_2 <- predict(WARp_obj, dSup, expSup) # dSup and expSup are chosen by user # Plots par(mfrow=c(1,2)) plot(forecast_1$dSup, forecast_1$pred.cdf, type="l", xlab="dSup", ylab="cdf") plot(forecast_1$dSup, forecast_1$pred.pdf, type="l", xlab="dSup", ylab="pdf") plot(forecast_2$dSup, forecast_2$pred.cdf, type="l", xlab="dSup", ylab="cdf") plot(forecast_2$dSup, forecast_2$pred.pdf, type="l", xlab="dSup", ylab="pdf")
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