after.minus.before {FeedbackTS}

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".

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).

Value

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

Author(s)

Samuel Soubeyrand [e-mail], Cindy E. Morris, E. Keith Bigg.

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

#### 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")