turnogram(series, intervals=c(1, length(series)/5), step=1, complete=FALSE,
two.tailed=TRUE, FUN=mean, plotit=TRUE, level=0.05, lhorz=TRUE,
lvert=FALSE, xlog=TRUE)
## S3 method for class 'turnogram':
summary(turno)
## S3 method for class 'turnogram':
plot(turno, level=0.05, lhorz=TRUE, lvert=TRUE, lcol=2,
llty=2, xlog=TRUE, \dots)
## S3 method for class 'turnogram':
identify(turno, lvert=TRUE, \dots)
## S3 method for class 'turnogram':
extract(turno, n, level=turno$level, FUN=turno$fun, drop=0)intervals ranges from 1 to the fifth of the total number of observationsstep=1. To limit calculation or for a first screenning with a large range in the intervals, use a higher value for stepcomplete=TRUE, a complete turnogram is calculated, showing mean, minimal and maximal curves. If it is FALSE (by default), only a simple turnogram always starting from the first observation is calculatedtwo.tailed=TRUE (by default), the monotony index is tested with a bilateral test, otherwise, a left-sided test is usedFUN(x, na.rm, ...). The most used function is mean() (by default), but it is also possible to keep only the first value with first()plotit=TRUE (by default), the graph of the turnogram is also plottedlevel=0.05, corresponding to a test with P = 5%lhorz=TRUE (by default) then one (left-sided test), or two (two-sided test) horizontal lines are drawn on the graph, indicating the significant level of the test given by the argument level. Any point above the single line, orlvert=TRUE (by default, except for turnogram() function), a vertical line is drawn, indicating the time interval that corresponds to the maximum information and it is also the automatic level of extraction unless this value islhorz=TRUE) and the vertical line indicating the extraction level (if lvert=TRUE). By default, color 2 is usedxlog=TRUE (by default), then the x-axis is expressed in logarithms. Otherwise, a linear scale is usedturnogram()n=NULL (by default) to use all observations of the seriesdrop=0: no observations are droppedprint(), summary(), plot(), identify() and extract().turnpoints()). If a series has a lot of erratic peaks and pits that alternate with a high frequency, it is more difficult to interpret than a more monotonous series. These erratic fluctuations can be eliminated by changing the scale of observation (keeping one observation every two, three, four,... from the original series). The turnogram resample the original series this way, and calculate a monotony index for each resampled subseries. This monotony index quantifies the number of peaks and pits presents in the series, compared to the total number of observations. The Gleissberg distribution (see pgleissberg()) indicates the probability to have such a number of extrema in a series given it is purely random. It is possible to test monotony indices: is it a random series or not (two-sided test), or is more monotonous than a random series (left-sided test) thanks to a Chi-2 test proposed by Wallis & Moore (1941).
There are various turnograms depending on the way the observations are aggregated inside each time interval. For instance, if one consider one observation every three from the original series, each group of three observations can be aggregated in several different ways. One can take the mean of the three observation, or the median value, or the sum,... One can also decide not to aggregate observations, but to drop some of them. Hence, one can take only the first or the last observation of the group. All these options can be choosen by defining the argument FUN=.... A simple turnogram correspond to the change of the monotony index with the scale of observation, stating always from the first observation. One could also decide to start from the second, or the third observation for an aggregation of the observations three by three... and result could be somewhat different. A complete turnogram investigates all possibles combinations (observation scale versus starting point for the aggregation) and trace the maximal, minimal and mean curves for the change of the monotony index. It is thus more informative than the simple turnogram. However, it takes much more time to compute.
The most obvious use of the turnogram is for the pretreatment of continuously sampled data. It helps in deciding which is the optimal sampling interval for the series to bear as most information as possible while keeping the dataset as small as possible. It is also interesting to compare the turnogram with other functions like the variogram (see vario()) or the spectrogram (see spectrum()).pgleissberg, turnpoints, first, last, vario, spectrumdata(bnr)
# Let's transform series 4 into a time series (supposing it is regular)
bnr4 <- as.ts(bnr[, 4])
plot(bnr4, type="l", main="bnr4: raw data", xlab="Time")
# A simple turnogram is calculated
bnr4.turno <- turnogram(bnr4)
summary(bnr4.turno)
# A complete turnogram confirms that "level=3" is a good value:
turnogram(bnr4, complete=TRUE)
# Data with maximum info. are extracted (thus taking 1 every 3 observations)
bnr4.interv3 <- extract(bnr4.turno)
plot(bnr4, type="l", lty=2, xlab="Time")
lines(bnr4.interv3, col=2)
title("Original bnr4 (dotted) versus max. info. curve (plain)")
# Choose another level (for instance, 6) and extract the corresponding series
bnr4.turno$level <- 6
bnr4.interv6 <- extract(bnr4.turno)
# plot both extracted series on top of the original one
plot(bnr4, type="l", lty=2, xlab="Time")
lines(bnr4.interv3, col=2)
lines(bnr4.interv6, col=3)
legend(70, 580, c("original", "interval=3", "interval=6"), col=1:3, lty=c(2, 1, 1))
# It is hard to tell on the graph which series contains more information
# The turnogram shows us that it is the "interval=3" one!Run the code above in your browser using DataLab