# MeanDurUnder: Mean Duration of sojourn under a treshold In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

## Description

Plot the mean duration of sojourn under thresholds for an observed time series and a simulated one with respect to teh empirical cumulative distribution function (cdf). Confidence intervals are plotted too.

## Usage

 `1` ```MeanDurUnder(data, data.sim, u, alpha = 0.05,col="red",plot=TRUE) ```

## Arguments

 `data` observed (or reference) time series, array of dimension T*N.samples*1 `data.sim` simulated time series, array of dimension T*N.sim*1. N.sim have to be K*N.samples with K large enough (for instance, K=100) `u` vector of thresholds `alpha` 1-confidence level for confidence intervals. Default = 0.05 `col` color of the lines for simulated data, default is red `plot` statistic are plotted if TRUE (default)

## Value

Returns a plot and a list including ..\$F : empirical cdf of data for levels u ..\$mdu.data : mean duration under levels u for data ..\$F.sim : empirical cdf of simulations for levels u ..\$mdu.sim : mean duration under levels u for simulations ..\$CI : confidence intervals of mean duration under levels u for simulations

## Author(s)

Valerie Monbet, [email protected]

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```data(meteo.data) data = array(meteo.data\$temperature,c(31,41,1)) k = 40 T = dim(data)[1] N.samples = dim(data)[2] d = dim(data)[3] M = 2 order = 2 theta.init = init.theta.MSAR(data,M=M,order=order,label="HH") mod.hh= NULL mod.hh\$theta = theta.init mod.hh\$theta\$A = matrix(c(0.40,0.88,-.09,-.13),2,2) mod.hh\$theta\$A0 = matrix(c(6.75,1.08),2,1) mod.hh\$theta\$sigma = matrix(c(1.76,3.40),2,1) mod.hh\$theta\$prior = matrix(c(0.37,0.63),2,1) mod.hh\$theta\$transmat = matrix(c(0.82,0.09,0.18,0.91),2,2) B.sim = 20*N.samples Y0 = array(data[1:2,sample(1:dim(data)[2],B.sim,replace=TRUE),],c(2,B.sim,1)) Y.sim = simule.nh.MSAR(mod.hh\$theta,Y0=Y0,T,N.samples=B.sim) u = seq(min(data),max(data),length.out=30) MeanDurUnder(data,Y.sim\$Y,u) ```