Berkowitz: Berkowitz test

Description Usage Arguments Details Value Author(s) References Examples

Description

Implements Berkowitz test (2001) for density evaluation.

Usage

1
Berkowitz(ydata, yhatdata, rep, ...)

Arguments

ydata

a data frame containing the real values of the dependent varible.

yhatdata

a data frame containing the fitted values of the dependent varible.

rep

number of uniform distirbution drawings.

...

not used.

Details

Diebold et al. (1998) proposed a density evaluation method which consists in computing the sequence of cumulative probability of the observed counts under the assumed forecast distribution (Probability Transform Integral-PIT). If the density fit is adequate this sequence will be uniformly distributed and will have no-autocorrelation left neither in level nor when raised to integer powers. For this purpose intuitive graphical methods such as correlograms on the basis of the usual Bartlett confidence intervals, histograms and quantile-quantile (QQ) plots are used. In the case of discrete data Heinen et al. (2007) propose the use of a uniform zero-one continued extension as suggested by Denuit and Lambert (2005). Finally instead of using graphical tools for detecting uniformity and independence, Berkowitz (2001) applied a formal test for normality and independence of the inverse standard cumulative normal transform of the PIT sequence through the estimation of an AR(1) specification and the use of an LR test to the coefficients.

Value

P-value of the Likelihood Ratio test statistic based on the chi-square distribution with 3 degress of freedom.

Author(s)

Siakoulis Vasileios

References

Examples

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data(polio)

#Create time trend and seasonality variables
trend=(1:168/168)
cos12=cos((2*pi*(1:168))/12)
sin12=sin((2*pi*(1:168))/12)
cos6=cos((2*pi*(1:168))/6)
sin6=sin((2*pi*(1:168))/6)

polio_data<-data.frame(polio, trend , cos12, sin12, cos6, sin6)
mod1 <- acp(polio~-1+trend+cos12+sin12+cos6+sin6,data=polio_data, p = 1 ,q = 2)
summary(mod1)
Berkowitz(polio_data[[1]],fitted(mod1),50)

acp documentation built on May 2, 2019, 9:59 a.m.

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