FeedbackTS (version 1.5)

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 KDD object or a KDD.yearly.average object.

operator

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

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.

If operator = "dmgiv" (difference of means of greater indicator values), the raw values \(y_{i-K},\ldots,y_{i+K}\) are used to compute the difference: $$ D_i=\left(\frac{1}{K}\sum_{k=1}^K 1(y_{i+k}>y_{i-k})\right) - \left(\frac{1}{K}\sum_{k=1}^K 1(y_{i-k}>y_{i+k})\right). $$

References

Soubeyrand, S., Morris, C. E. and Bigg, E. K. (2014). Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environmental Modelling and Software 61: 78-86.

See Also

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

Examples

# NOT RUN {
#### 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")
# }