AutoD2, CrossD2 or CenterD2 analysis of a multiple time-series
Compute and plot multiple autocorrelation using Mahalanobis generalized distance D2. AutoD2 uses the same multiple time-series. CrossD2 compares two sets of multiple time-series having same size (same number of descriptors). CenterD2 compares subsamples issued from a single multivariate time-series, aiming to detect discontinuities.
AutoD2(series, lags=c(1, nrow(series)/3), step=1, plotit=TRUE,
add=FALSE, ...)
CrossD2(series, series2, lags=c(1, nrow(series)/3), step=1,
plotit=TRUE, add=FALSE, ...)
CenterD2(series, window=nrow(series)/5, plotit=TRUE, add=FALSE,
type="l", level=0.05, lhorz=TRUE, lcol=2, llty=2, ...)series |
regularized multiple time-series |
series2 |
a second set of regularized multiple time-series |
lags |
minimal and maximal lag to use. By default, 1 and a third of the number of observations in the series respectively |
step |
step between successive lags. By default, 1 |
window |
the window to use for CenterD2. By default, a fifth of the total number of observations in the series |
plotit |
if |
add |
if |
type |
The type of line to draw in the CenterD2 graph. By default, a line without points |
level |
The significance level to consider in the CenterD2 analysis. By default 5% |
lhorz |
Do we have to plot also the horizontal line representing the significance level on the graph? |
lcol |
The color of the significance level line. By default, color 2 is used |
llty |
The style for the significance level line. By default: |
... |
additional graph parameters |
An object of class 'D2' which contains:
lag |
The vector of lags |
D2 |
The D2 value for this lag |
call |
The command invoked when this function was called |
data |
The series used |
type |
The type of 'D2' analysis: 'AutoD2', 'CrossD2' or 'CenterD2' |
window |
The size of the window used in the CenterD2 analysis |
level |
The significance level for CenterD2 |
chisq |
The chi-square value corresponding to the significance level in the CenterD2 analysis |
units.text |
Time units of the series, nicely formatted for graphs |
If data are too heterogeneous, results could be biased (a singularity matrix appears in the calculations).
Frédéric Ibanez (ibanez@obs-vlfr.fr), Philippe Grosjean (phgrosjean@sciviews.org)
Cooley, W.W. & P.R. Lohnes, 1962. Multivariate procedures for the behavioural sciences. Whiley & sons.
Dagnélie, P., 1975. Analyse statistique à plusieurs variables. Presses Agronomiques de Gembloux.
Ibanez, F., 1975. Contribution à l'analyse mathématique des évènements en écologie planctonique: optimisations méthodologiques; étude expérimentale en continu à petite échelle du plancton côtier. Thèse d'état, Paris VI.
Ibanez, F., 1976. Contribution à l'analyse mathématique des évènements en écologie planctonique. Optimisations méthodologiques. Bull. Inst. Océanogr. Monaco, 72:1-96.
Ibanez, F., 1981. Immediate detection of heterogeneities in continuous multivariate oceanographic recordings. Application to time series analysis of changes in the bay of Villefranche sur mer. Limnol. Oceanogr., 26:336-349.
Ibanez, F., 1991. Treatment of the data deriving from the COST 647 project on coastal benthic ecology: The within-site analysis. In: B. Keegan (ed), Space and time series data analysis in coastal benthic ecology, p 5-43.
data(marphy)
marphy.ts <- as.ts(as.matrix(marphy[, 1:3]))
AutoD2(marphy.ts)
marphy.ts2 <- as.ts(as.matrix(marphy[, c(1, 4, 3)]))
CrossD2(marphy.ts, marphy.ts2)
# This is not identical to:
CrossD2(marphy.ts2, marphy.ts)
marphy.d2 <- CenterD2(marphy.ts, window=16)
lines(c(17, 17), c(-1, 15), col=4, lty=2)
lines(c(25, 25), c(-1, 15), col=4, lty=2)
lines(c(30, 30), c(-1, 15), col=4, lty=2)
lines(c(41, 41), c(-1, 15), col=4, lty=2)
lines(c(46, 46), c(-1, 15), col=4, lty=2)
text(c(8.5, 21, 27.5, 35, 43.5, 57), 11, labels=c("Peripheral Zone", "D1",
"C", "Front", "D2", "Central Zone")) # Labels
time(marphy.ts)[marphy.d2$D2 > marphy.d2$chisq]Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.