Function to create the normalized conditional (randomized) quantile residuals.
an object of class "glarma"
glarmaPredProb produces the non-randomized
probability integral transformation (PIT). It returns estimates of the
cumulative predictive probabilities as upper and lower bounds of a
collection of intervals. If the model is correct, a histogram drawn
using these estimated probabilities should resemble a histogram
obtained from a sample from the uniform distribution. This function
aims to produce observations which instead resemble a sample from a
normal distribution. Such a sample can then be examined by the usual
tools for checking normality, such as histograms, Q-Q normal plots and
for checking independence, autocorrelation and partial autocorrelation
plots, and associated portmanteau statistics.
For each of the intervals produced by
random uniform observation is generated, which is then converted to a
normal observation by applying the inverse standard normal
distribution function (that is
qnorm). The vector of
these values is returned by the function in the list element
rt. In addition non-random observations which should appear
similar to a sample from a normal distribution are obtained by
qnorm to the mid-points of the predictive distribution
intervals. The vector of these values is returned by the function in
the list element
A list consisting of two elements:
the normalized conditional (randomized) quantile residuals
the midpoints of the predictive probability intervals
Berkowitz, J. (2001) Testing density forecasts, with applications to risk management. Journal of Business \& Economic Statistics, 19, 465–474.
Dunn, Peter K. and Smyth, Gordon K. (1996) Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5, 236–244.
See also as
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data(DriverDeaths) y <- DriverDeaths[, "Deaths"] X <- as.matrix(DriverDeaths[, 2:5]) Population <- DriverDeaths[, "Population"] ### Offset included glarmamodOffset <- glarma(y, X, offset = log(Population/100000), phiLags = c(12), type = "Poi", method = "FS", residuals = "Pearson", maxit = 100, grad = 1e-6) rt <- normRandPIT(glarmamodOffset)$rt par(mfrow = c(2,2)) hist(rt, main = "Histogram of Randomized Residuals", xlab = expression(r[t])) box() qqnorm(rt, main = "Q-Q Plot of Randomized Residuals" ) abline(0, 1, lty = 2) acf(rt, main = "ACF of Randomized Residuals") pacf(rt, main = "PACF of Randomized Residuals")
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