Description Usage Arguments Details Value Author(s) References See Also Examples

Function to create the normalized conditional (randomized) quantile residuals.

1 | ```
normRandPIT(object)
``` |

`object` |
an object of class "glarma" |

The function `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 `glarmaPredProb`

, a
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
applying `qnorm`

to the mid-points of the predictive distribution
intervals. The vector of these values is returned by the function in
the list element `rtMid`

.

A list consisting of two elements:

`rt` |
the normalized conditional (randomized) quantile residuals |

`rtMid` |
the midpoints of the predictive probability intervals |

"William T.M. Dunsmuir" <w.dunsmuir@unsw.edu.au> and "David J Scott" <d.scott@auckland.ac.nz>

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 `glarmaPredProb`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
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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