Generates a 2k sample of test statistics projecting the stationary process using the random projections procedure.
rp.sample(y, k = 1, pars1 = c(100,1), pars2 = c(2,7), seed = NULL)A list with 2 real value vectors:
A vector with the Lobato and Velasco's statistics sample.
A vector with the Epps statistics sample.
a numeric vector or an object of the ts class containing a
stationary time series.
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.
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.
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.
An optional seed to use.
Alicia Nieto-Reyes and Asael Alonzo Matamoros
The rp.sample function generates `2k` tests statistics by projecting
the time series using `2k` stick breaking processes. First, the function
samples `k` stick breaking processes using pars1 argument. Then, projects
the time series using the sampled stick processes. Later, applies the Epps
statistics to the odd projections and the Lobato and Velasco’s statistics to
the even ones. Analogously, the function performs the three steps using also
pars2 argument
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).
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.
lobato.test, epps.test
# Generating an stationary ARMA process
y = arima.sim(100,model = list(ar = 0.3))
rp.sample(y)
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