FeedbackTS (version 1.2)

after.minus.before: Computation of after-before differences around key days

Description

Computation of after-before differences around key days using using data $K$ days before and after each key day.

Usage

after.minus.before(data, operator)

Arguments

data

either a KDD object, a KDD.yearly.average object, or a matrix with an odd number of rows corresponding built as the before.after slot of a

operator

a character string specifying the transformation of the raw values, must be one of "dmv" or "dmpiv".

Value

• A numeric vector providing for each key day the value of the after-before difference.

Details

If operator = "dmv" (difference of mean values), the raw values $y_{i-K},\ldots,y_{i+K}$ of the time series are used to compute the difference: $$D_i=\left(\frac{1}{K}\sum_{k=1}^K y_{i+k}\right) - \left(\frac{1}{K}\sum_{k=1}^K y_{i-k}\right)=\frac{1}{K}\sum_{k=1}^K (y_{i+k}-y_{i-k}),$$ where $i$ is the date of the key day, $K$ is the number of days considered after and before the key day (specified when data is provided). If operator = "dmpiv" (difference of means of positive indicator values), the raw values $y_{i-K},\ldots,y_{i+K}$ are used to compute the difference: $$D_i=\left(\frac{1}{K}\sum_{k=1}^K 1(y_{i+k}>0)\right) - \left(\frac{1}{K}\sum_{k=1}^K 1(y_{i-k}>0)\right)=\frac{1}{K}\sum_{k=1}^K {1(y_{i+k}>0)-1(y_{i-k}>0)},$$ where $1(\cdot)$ is the indicator function.

References

Soubeyrand, S., Morris, C. E. and Bigg, E. K. (in press). Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environmental Modelling and Software.

See Also

KDD, KDD.yearly.average, kdd.from.raw.data, rain.site.6008

Examples

#### load data for site 6008 (Callagiddy station)
data(rain.site.6008)

#### build KDD objects from raw data (site 6008: Callagiddy station)
## using a threshold value equal to 25
KDD=kdd.from.raw.data(raw.data=rain.site.6008,keyday.threshold=25,nb.days=20,
   col.series=5,col.date=c(2,3,4),na.rm=TRUE,filter=NULL)

#### compute and plot after-before differences of KDD 
par(mfrow=c(2,2), mar=c(5.1,4.1,4.1,4.1))

## using option dmpiv (difference of means of positive indicator values)
amb1=after.minus.before(KDD,"dmpiv")
plot(KDD["day"],amb1,type="l",xlab="Day",ylab="After-Before")
abline(h=0,lty="dashed",col="grey")
plot(KDD["day"],cumsum(amb1),type="l",xlab="Day",ylab="Cumul After-Before")
abline(h=0,lty="dashed",col="grey")

## using option dmv (difference of means of values)
amb2=after.minus.before(KDD,"dmv")
plot(KDD["day"],amb2,type="l",xlab="Day",ylab="After-Before")
abline(h=0,lty="dashed",col="grey")
plot(KDD["day"],cumsum(amb2),type="l",xlab="Day",ylab="Cumul After-Before")
abline(h=0,lty="dashed",col="grey")