nortsTest (version 1.1.2)

rp.test: The k random projections test for normality.

Description

Performs the random projection test for normality. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.

Usage

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

Value

A list with class "h.test" containing the following components:

statistic:

an integer value with the amount of projections per test.

parameter:

a text that specifies the p.value mixing FDR method.

p.value:

the FDR mixed p-value for the test.

alternative:

a character string describing the alternative hypothesis.

method:

a character string “k random projections test”.

data.name:

a character string giving the name of the data.

Arguments

y

a numeric vector or an object of the ts class containing a stationary time series.

k

an integer that determines the `2k` random projections are used for every type of test. The `pars1` argument generates the first `k` projections, and `pars2` generates the later `k` projections. By default, k = 1.

FDR

a logical value for mixing the p.values using a False discovery rate method. If FDR = TRUE, then the p.values are mixed using Benjamin and Yekutieli (2001) False discovery Rate method for dependent procedures, on the contrary, it applies Benjamini and Hochberg (1995) procedure. By default, FDR = TRUE.

pars1

an optional real vector with the shape parameters of the beta distribution used for the first `k` random projections 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 to compute the last `k` random projections. By default, pars2 = c(2,7) where, shape1 = 2 and shape2 = 7.

seed

An optional seed to use.

Author

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

Details

The random projection test generates `2k` random projections of `y`. Applies Epps statistics to the odd projections and Lobato and Velasco’s statistics to the even ones. Computes the `2k` p.values using an asymptotic chi-square distribution with two degrees of freedom. Finally, mixes the p.values using a false discover rate procedure. By default, mixes the p.values using Benjamin and Yekutieli’s (2001) method.

The function uses beta distributions for generating the `2k` random projections. By default, uses a beta(shape1 = 100,shape = 1) distribution contained in pars1 argument to generate the first `k` projections. For the later `k` projections the functions uses a beta(shape1 = 2,shape = 7) distribution contained in pars2 argument.

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

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.

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

Benjamini, Y., and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics. 29, 1165–1188. Doi:10.1214/aos/1013699998.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 75, 800–803. Doi:10.2307/2336325.

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

See Also

lobato.test, epps.test

Examples

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