nortsTest (version 1.1.2)

epps.test: The asymptotic Epps and Pulley Test for normality.

Description

Performs the asymptotic Epps test of normality for univariate time series. Computes the p-value using the asymptotic Gamma Distribution.

Usage

epps.test(y, lambda = c(1,2))

Value

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

statistic:

the Epps statistic.

parameter:

the test degrees freedoms.

p.value:

the p value.

alternative:

a character string describing the alternative hypothesis.

method:

a character string “Epps 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.

lambda

a numeric vector for evaluating the characteristic function. This values could be selected by the user for a better test performance. By default, the values are `c(1,2)`, another plausible option is to select random values.

Author

Asael Alonzo Matamoros and Alicia Nieto-Reyes.

Details

The Epps test minimize the process' empirical characteristic function using a quadratic loss in terms of the process two first moments. Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014) upgrade the test implementation by allowing the option of evaluating the characteristic function with random values. The amoebam() function of Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007), performs the optimal search.

References

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

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.

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007). Numerical Recipes. The Art of Scientific Computing. Cambridge University Press.

See Also

lobato.test

Examples

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

# Epps tests with random lambda values
y = arima.sim(100,model = list(ar = c(0.3,0.2)))
epps.test(y, lambda = rnorm(2,mean = 1,sd = 0.1))