diffsign.test: the Differents-Sign Test of Statistical Independence In spgs: Statistical Patterns in Genomic Sequences

Description

Tests for a trend in a data series by comparing the number of positive differences between successive elements in the series to the number expected in an i.i.d. series.

Usage

 `1` ```diffsign.test(x) ```

Arguments

 `x` a numeric vector or univariate time series.

Details

Perform a test for trend based on the signs of successive differences in a data series. #this function counts the number of positive successive differences in the data, standardises #it to have mean 0 and variance 1 and asymptotically tests it against a standard normal distribution. the test statistic is:

D = (pd - mu)/sigma, where
pd is the number of positive differences in the data series,
mu = (n-1)/2,
sigma = sqrt((n+1)/12) and
n is the number of points in the data series.

The test is set up as follows:

H0: the data series is i.i.d. (not trending)
H1: the data series is not i.i.d. (trending)

Value

A list with class "htest" containing the following components:

 `statistic` the value of the test statistic. `p.value` the p-value of the test. `method` a character string indicating what type of test was performed. `data.name` a character string giving the name of the data. `n` the number of points in the data series. `mu` The expected number of positive differences that would be seen in an i.i.d. series. `sigma` The standard deviation of the number of positive differences that would be seen in an i.i.d. series.

Note

Missing values are not handled.

Points followed by a point having the exact same value are removed from the data series before computing the test statistic.

This test is useful for detecting linear trends in data series.

Author(s)

Andrew Hart and Servet Mart<ed>nez

References

Brockwell, Peter J., Davis, Richard A. (2002) Introduction to Time Series and Forecasting. Springer Texts in Statistics, Springer-Verlag, New York.

`turningpoint.test`, `rank.test`, `lb.test` `markov.test`, `diid.test`,
 ```1 2 3``` ```#Generate an IID standard normal sequence n <- rnorm(1000) diffsign.test(n) ```