epps.statistic {nortsTest}

Estimates the Epps statistic.

Description

Estimates the Epps statistic minimizing the quadratic loss of the process' characteristic function in terms of the first two moments.

Usage

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

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.

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.

This function is the equivalent of Sub in Nieto-Reyes, A., Cuesta-Albertos, J. & Gamboa, F. (2014). This function uses a quadratic optimization solver implemented by Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (2007).

Value

a real value with the Epps test's statistic.

Author(s)

Alicia Nieto-Reyes and Asael Alonzo Matamoros.

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.statistic

Examples

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