applySnht: Conduct the standard normal homogeneity test
In hydro-giub/hydroBE: Miscellaneous Functions of the Group of Hydrology Bern

Description Usage Arguments Details Value Author(s) References See Also Examples

The standard normal homogeneity test (SNHT) tries to detect a breakpoint concerning the mean value of a time series, usually in combination with a homogeneous reference series. If so, the goal is to detect artificial instationarities introduced by e.g. station relocations or sensor drifts.

1	applySnht(y, x, method, omit = 0)

`y`	numeric vector. The candidate series to be tested.
`x`	numeric vector. The reference series (often this series is a composite of nearby observation sites, e.g. from weather stations).
`method`	string. Must be either 'ratio' or 'diff' to specify whether to take ratios or differences between the candidate and reference series.
`omit`	integer. Number of leading and trailing observations to omit when estimating the most probable time point of change.

If x is missing, the test is conducted on the candidate series y only. Since the SNHT is known to be overly sensitive to detect breakpoints at the beginning and end of the series, the argument omit can be used to exclude the first and last few time steps while extracting the maximum of the test statistic.

List with entries:

`i`	integer. The index of the most probable breakpoint, i.e. the last time step before the break occurs.
`test`	logical vector. Significance of the most probable breakpoint `i` with respect to the levels 0.1, 0.08, 0.06, 0.05, 0.025, and 0.01. The critical values are taken from Khaliq and Ouarda (2007).
`tv`	numeric vector. The test statistic.
`q`	numeric vector. The q series according to `method`; if `x` is missing, `q` equals `y` with mean zero and standard deviation one.

Original code provided by Pascal H.

Alexanderson, H. (1986). "A homogeneity test applied to precipitation data". International Journal of Climatology.

Khaliq, M. N., and T. B. M. J. Ouarda (2007). "On the critical values of the standard normal homogeneity test (SNHT)". International Journal of Climatology.

testLinearTrend and testBreakpoint for other statistical tests concerning the detection of instationarities in time series (but without the option to include a reference series).

n <- 40
x <- c(rnorm(n/2,2,0.15),rnorm(n/2,2.5,0.15))
y <- rnorm(n,2,0.15)
snht <- applySnht(x=x,y=y,method='diff',omit=2)
i <- snht$i
plot(x,type='l')
abline(v=i+0.5,lty=3)
lines(x=c(1,i),y=rep(mean(x[1:i]),2),col=2)
lines(x=c(i+1,n),y=rep(mean(x[(i+1):n]),2),col=2)