Performs the approximated Epps and Pulley's test of normality for univariate time series. Computes the p-value using Psaradakis and Vavra's (2020) sieve bootstrap procedure.
epps_bootstrap.test(y, lambda = c(1,2), reps = 500, h = 100, seed = NULL)A list with class "h.test" containing the following components:
the sieve bootstrap Epps and Pulley's statistic.
the p value for the test.
a character string describing the alternative hypothesis.
a character string “Sieve-Bootstrap Epps' test”.
a character string giving the name of the data.
a numeric vector or an object of the ts class containing a stationary
time series.
a numeric vector for evaluating the characteristic function.
an integer with the total bootstrap repetitions.
an integer with the first burn-in sieve bootstrap replicates.
An optional seed to use.
Asael Alonzo Matamoros and Alicia Nieto-Reyes.
The Epps test minimize the process' empirical characteristic function using a quadratic loss in terms of the process two first moments, Epps, T.W. (1987). Approximates the p-value using a sieve-bootstrap procedure Psaradakis, Z. and Vávra, M. (2020).
Psaradakis, Z. and Vávra, M. (2020) Normality tests for dependent data: large-sample and bootstrap approaches. Communications in Statistics-Simulation and Computation 49 (2). ISSN 0361-0918.
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.statistic, epps.test
# Generating an stationary arma process
y = arima.sim(300, model = list(ar = 0.3))
epps_bootstrap.test(y, reps = 1000)
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