# pTimEv: Model stationnary testing In GPoM: Generalized Polynomial Modelling

## Description

Estimate the parameters variations of a model of canonical form considering a sliding window on an external dataset.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```pTimEv( TS, nVar, dMax, TSdate, whatTerms = NULL, wlength = 1000, onestep = 100, removeExtr = 1 ) ```

## Arguments

 `TS` The time series to be tested `nVar` Number of variables considered in the polynomial formulation. `dMax` Maximum degree of the polynomial formulation. `TSdate` The time vector `whatTerms` The terms to be considered in the analysis. Note that these are organised following the convention defined by poLabs(nVar,dMax). Since only the structure is required, if coefficients are provided, these are transformed to 1. `wlength` The window length `onestep` Step length between two estimations `removeExtr` Ratio of estimated values to be removed (if chosen equal to 0.1, only 90 disersion will be kept)

## Value

A list containing:

`\$slidingoutGM` An n*(pMax+1) matrix presenting the pMax estimated parameters p1(t), p2(t) etc. column by column. The residual signal epsilon(t) is provided in the last (i.e. pMax + 1) column. Each line correspond to one date provided in `\$TSdate`

`\$TSdate` A time vector relating to the estimates presented in `\$slidingoutGM`

`\$W` A vector providing the output values that can kept (=1) or must be removed (=0)

`\$whatTerms` A vector recalling the terms taken into account in the analysis (their order refers to `poLabs(nVar,dMax)` function)

`\$param` A vector with the parameter values used to apply the function: nVar, dMax, wlength, onestep, removeExtr

## Author(s)

Sylvain Mangiarotti

`autoGPoMoSearch`, `gPoMo`, `poLabs`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```#Example data(TS) plot(TS[,1], TS[,2], type='l') nVar <- 3 dMax <- 2 pMax <- choose(nVar+dMax,dMax) whatTerms <- c(1,1,0,1,1,1,1,1,1,1) # apply pTimEv statio <- pTimEv(TS[,2], nVar, dMax, TS[,1], whatTerms = whatTerms, wlength = 1000, onestep = 20, removeExtr = 0.15) # Plot the results dev.new() layout(matrix(1:12, nrow=4, ncol=3, byrow = TRUE)) what <- which(statio\$whatTerms!=0) for (i in what) { plot(statio\$TSdate[statio\$W==1], statio\$slidingoutGM[statio\$W==1,i], xlab='TSdate', ylab='coeff', main=poLabs(nVar,dMax)[i]) } plot(statio\$TSdate[statio\$W==1], statio\$slidingoutGM[statio\$W==1,pMax+1], xlab='date', ylab='Epsilon', main='Resid', log = 'y') ```