Wallis and Moore Phase-Frequency Test
Performes the non-parametric Wallis and Moore phase-frequency test for testing the H0-hypothesis, whether the series comprises random data, against the HA-Hypothesis, that the series is significantly different from randomness (two-sided test).
wm.test(x)
x |
a vector or a time series object of class "ts" |
The test statistic of the phase-frequency test for n > 30 is calculated as:
z = abs(h - (2 * n - 7) / 3) / sqrt((16 * n - 29)/ 90)
where h denotes the number of phases, whereas the first and the last phase is not accounted. The z-statistic is normally distributed. For n ≤ 30 a continuity correction of -0.5 is included in the denominator.
An object of class "htest"
method |
a character string indicating the chosen test |
data.name |
a character string giving the name(s) of the data |
statistic |
the Wallis and Moore z-value |
alternative |
a character string describing the alternative hypothesis |
p.value |
the p-value for the test |
NA values are omitted. Many ties in the series will lead to reject H0 in the present test.
L. Sachs (1997), Angewandte Statistik. Berlin: Springer.
C.-D. Schoenwiese (1992), Praktische Statistik. Berlin: Gebr. Borntraeger.
W. A. Wallis and G. H. Moore (1941): A significance test for time series and other ordered observations. Tech. Rep. 1. National Bureau of Economic Research. New York.
## Example from Schoenwiese (1992, p. 113) ## Number of frost days in April at Munich from 1957 to 1968 ## z = -0.124, Accept H0 frost <- ts(data=c(9,12,4,3,0,4,2,1,4,2,9,7), start=1957) wm.test(frost) ## Example from Sachs (1997, p. 486) ## z = 2.56, Reject H0 on a level of p < 0.05 x <- c(5,6,2,3,5,6,4,3,7,8,9,7,5,3,4,7,3,5,6,7,8,9) wm.test(x) wm.test(nottem)
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