rp.test: The k random projections test for normality

In nortsTest: Assessing Normality of Stationary Process

Description

Performs the random projection test for normality. The null hypothesis (H0) is that the given data follows a stationary Gaussian process, and k is the number of used random projections.

Usage

rp.test(y,k = 16,FDR = TRUE,pars1 = c(100,1),pars2  = c(2,7),seed = NULL)

Arguments

y	a numeric vector or an object of the ts class containing a stationary time series.
k	an integer with the number of random projections to be used, by default k = 16.
FDR	a logical value for mixing the p-values using a dependent False discovery rate method. If FDR =TRUE, then the p-values are mixed using a False discovery Rate method, on the contrary it applies the Benjamin and Yekuteli (2001) procedure. By default FDR = TRUE.
pars1	an optional real vector with the shape parameters of the beta distribution used for the odd number random projection. By default, pars1 = c(100,1) where, shape1 = 100 and shape2 = 1.
pars2	an optional real vector with the shape parameters of the beta distribution used for the even number random projection. By default, pars2 = c(2,7) where, shape1 = 2 and shape2 = 7.
seed	An optional seed to use.

Details

The random projection test generates k independent random projections of the process. A Lobato and Velasco's test are applied to the first half of the projections, and an Epps test for the other half. Then, a False discovery rate is used for mixing the obtained p.values

For generating the k random projections a beta distribution is used. By default a beta(shape1 = 100,shape = 1) and a beta(shape1 = 2,shape = 7) are used to generate the odd and even projections respectively. For using a different parameter set, change pars1 or pars2.

The test was proposed by Nieto-Reyes, A.,Cuesta-Albertos, J. & Gamboa, F. (2014).

Value

a h.test class with the main results of the Epps hypothesis test. The h.test class have the following values:

• "k"The number of used projections

• "lobato"The average Lobato and Velasco's test statistics of the k projected samples

• "epps"The average Epps test statistics of the k projected samples

• "p.value"The mixed p value

• "alternative"The alternative hypothesis

• "method"The used method: rp.test

• "data.name"The data name.

Author(s)

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

References

Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). A random-projection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 1683-1698.

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.test epps.test

Examples

# Generating an stationary arma process
y = arima.sim(100,model = list(ar = 0.3))
rp.test(y,k = 4)

nortsTest documentation built on Aug. 16, 2021, 5:06 p.m.