normal.test: The normality test for stationary process
In nortsTest: Assessing Normality of Stationary Process

Description Usage Arguments Details Value Author(s) References See Also Examples

Perform a normality test. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.

1 2	normal.test(y,normality = c("epps","lobato","vavra","rp","jb","ad","shapiro"), alpha = 0.05)

`y`	a numeric vector or an object of the `ts` class containing a stationary time series.
`normality`	A character string naming the desired test for checking normality. Valid values are `"epps"` for the Epps, `"lobato"` for Lobato and Velasco's,`"vavra"` for the Psaradakis and Vavra, `"rp"` for the random projections, `"jb"` for the Jarque and Beras, `"ad"` for Anderson Darling test, and `"shapiro"` for the Shapiro-Wilk's test. The default value is `"epps"` test.
`alpha`	Level of the test, possible values range from 0.01 to 0.1. By default `alpha = 0.05` is used.

Several different tests are available: "lobato", "epps", "vavras" and "rp" test are for testing normality in stationary process. "jb", "ad", and "shapiro" tests are for numeric data. In all cases, the alternative hypothesis is that y follows a Gaussian process. By default, alpha = 0.05 is used to select the more likely hypothesis.

An h.test class with the main results of normal hypothesis test.

Asael Alonzo Matamoros

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.

Psaradakis, Z. & Vavra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 50-60.

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.

Patrick, R. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Journal of Applied Statistics. 31, 115-124.

Cromwell, J. B., Labys, W. C. & Terraza, M. (1994). Univariate Tests for Time Series Models. Sage, Thousand Oaks, CA. 20-22.

uroot.test,seasonal.test

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

# normal random sample
y = rnorm(100)
normal.test(y,normality = "shapiro")

# exponential random sample
y = rexp(100)
normal.test(y,normality = "ad")