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.
diffsign.test(x)A list with class "htest" containing the following components:
the value of the test statistic.
the p-value of the test.
a character string indicating what type of test was performed.
a character string giving the name of the data.
the number of points in the data series.
The expected number of positive differences that would be seen in an i.i.d. series.
The standard deviation of the number of positive differences that would be seen in an i.i.d. series.
a numeric vector or univariate time series.
Andrew Hart and Servet Martínez
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:
\(H_0\): the data series is i.i.d. (not trending)
\(H_1\): the data series is not i.i.d. (trending)
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,
#Generate an IID standard normal sequence
n <- rnorm(1000)
diffsign.test(n)
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