removetrendMPst: Median polish trend
In STMedianPolish: Spatio-Temporal Median Polish

Description Usage Arguments Details Value References Examples

Direct method to remove the trend of spatio - temporal data througth median polish.

1	removetrendMPst(MPST,eps=0.01, maxiter=10L)

`MPST`	object of class `ConstructMPst`
`eps`	real number greater than `0`, default 0.01. A tolerance for convergence of median polish.
`maxiter`	the maximum number of iterations, default 10.

Following the Berke's approach (Berke, 2001) to remove spatial trend, Martinez et al.(2017) used a structure of four dimensions to apply median polish tecnique.

For data ≤ft\{Y(\mathbf{s}_{abc},t), a=1,...,U; b=1,...,V; c=1,...,W, t=1,...,n \right\} , a spatial and temporal process is given by:

Y(\mathbf{s}_{abc},t)= μ_{y}(\mathbf{s}_{abc},t) + δ _{abct}

where

μ _{y}(\mathbf{s}_{abc},t)= μ +α _{a} + β _{b} + ξ _{c} + τ _{t}

and δ _{abct} is a fluctuation arising from natural variability and from the measurement process. Additionally, μ is an overall mean, α_{a} is the a-th row effect, β_{b} is the effect b-th column effect, ξ_{c} is the c-th layer effect and τ _{t} is the t-th time effect.

data.frame with the following fields:

`ET`	indicate the time of a observation.
`x`	spatial coordinate x.
`y`	spatial coordinate y.
`z`	spatial coordinate z.
`Trend`	trend calculated through median polish space - time.
`Value`	observed values.
`Residual`	Residual = Value-Trend.

Martínez, W. A., Melo, C. E., & Melo, O. O. (2017). Median Polish Kriging for space–time analysis of precipitation Spatial Statistics, 19, 1-20. [link]

Berke, O. (2001). Modified median polish kriging and its application to the wolfcamp - aquifer data. Environmetrics, 12(8):731-748.[link]

## Not run:
library(zoo)
data(Metadb)
#records of monthly precipitation from january 2007 to january 2010
Metadb<-Metadb[,c(1:4,89:125)]
x<-matrix(0,1,37)
for(i in 1:37){
 x[,i] <- 2007 + (seq(0, 36)/12)[i]
}
x<-as.Date (as.yearmon(x), frac = 1)
time = as.POSIXct(x, tz = "GMT")

MPST<-ConstructMPst(Metadb[,-c(1:4)],time,pts=Metadb[,2:4],Delta=c(7,6,5))
residual<-removetrendMPst(MPST,eps=0.01, maxiter=2)
## End(Not run)