bartels.test: Bartels Test for Randomness

In trend: Non-Parametric Trend Tests and Change-Point Detection

Bartels Test for Randomness

Description

Performes a rank version of von Neumann's ratio test as proposed by Bartels. The null hypothesis of randomness is tested against the alternative hypothesis

Usage

bartels.test(x)

Arguments

x	a vector of class "numeric" or a time series object of class "ts"

Details

In this function, the test is implemented as given by Bartels (1982), where the ranks r_1, \ldots, r_n of the X_i, \ldots, X_n are used for the statistic:

T = \frac{\sum_{i=1}^n (r_i - r_{i+1})^2}{\sum_{i=1}^n (r_i - \bar{r})^2}

As proposed by Bartels (1982), the p-value is calculated for sample sizes in the range of (10 \le n < 100) with the non-standard beta distribution for the range 0 \le x \le 4 with parameters:

a = b = \frac{5 n \left( n + 1\right) \left(n - 1\right)^2} {2 \left(n - 2\right) \left(5n^2 - 2n - 9\right)} - \frac{1}{2}

For sample sizes n \ge 100 a normal approximation with N(2, 20/(5n + 7)) is used for p-value calculation.

Value

A list with class "htest"

data.name	character string that denotes the input data
p.value	the p-value
statistic	the test statistic
alternative	the alternative hypothesis
method	character string that denotes the test

Note

The current function is for complete observations only.

References

R. Bartels (1982), The Rank Version of von Neumann's Ratio Test for Randomness, Journal of the American Statistical Association 77, 40–46.

See Also

ww.test, wm.test

Examples

# Example from Schoenwiese (1992, p. 113)
## Number of frost days in April at Munich from 1957 to 1968
## 
frost <- ts(data=c(9,12,4,3,0,4,2,1,4,2,9,7), start=1957)
bartels.test(frost)

## Example from Sachs (1997, p. 486)
x <- c(5,6,2,3,5,6,4,3,7,8,9,7,5,3,4,7,3,5,6,7,8,9)
bartels.test(x)

## Example from Bartels (1982, p. 43)
x <- c(4, 7, 16, 14, 12, 3, 9, 13, 15, 10, 6, 5, 8, 2, 1, 11, 18, 17)
bartels.test(x)
 

trend documentation built on Oct. 10, 2023, 9:06 a.m.