normal.test  R Documentation 
Perform a normality test. The null hypothesis (H0) is that the given data follows a stationary Gaussian process.
normal.test(y, normality = c("epps","lobato","vavra","rp","jb","ad","shapiro"),
alpha = 0.05)
y 
a numeric vector or an object of the 
normality 
A character string naming the desired test for checking normality. Valid values are

alpha 
Level of the test, possible values range from 0.01 to 0.1. By default 
"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.
A list with class "h.test"
containing the following components:
statistic: 
the test statistic. 
parameter: 
the test degrees freedoms. 
p.value: 
the pvalue for the test. 
alternative: 
a character string describing the alternative hypothesis. 
method: 
a character string with the test name. 
data.name: 
a character string giving the name of the data. 
Asael Alonzo Matamoros
Epps, T.W. (1987). Testing that a stationary time series is Gaussian. The Annals of Statistic. 15(4), 16831698.
Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671689.
Psaradakis, Z. & Vávra, M. (2017). A distance test of normality for a wide class of stationary process. Journal of Econometrics and Statistics. 2, 5060.
NietoReyes, A., CuestaAlbertos, J. & Gamboa, F. (2014). A randomprojection based test of Gaussianity for stationary processes. Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124141.
Patrick, R. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Journal of Applied Statistics. 31, 115124.
Cromwell, J. B., Labys, W. C. & Terraza, M. (1994). Univariate Tests for Time Series Models. Sage, Thousand Oaks, CA. 2022.
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")
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