NHMSAR (version 1.1)

valid_all: Statistics plotting for validation of MSAR models

Description

plots some functional statistics to help to valid MSAR models: qqplot, covariance function, mean duration of sojourn over and under a threshold. For each of them the empirical statistic of the observed time series is plotted as well as the simulated one with $(1-\alpha)$-fluctuation intervals.

Usage

valid_all(data, simu, root.filename = " ", path = NULL, title = "", 
  id = 1, alpha = 0.05, save = FALSE,output=FALSE)

Arguments

data

observed (or reference) time series, array of dimension T*N.samples*d

simu

simulated time series, array of dimension T*N.sim*d. N.sim have to be K*N.samples with K large enough (for instance, K=100)

title

title of plots

id

component to be considered when the data is multivariate (d>1). Default d=1.

alpha

level for the $(1-\alpha)$-fluctuation intervals

save

if save=TRUE plots are saved into .eps files

root.filename

root file name for saving plots

path

path of folder where to save the files

output

if TRUE some statistics are returned.

Value

• Returns plots and
• qqp
  statistics of marginal distributions
• C
  statistics of correlation functions
• ENu.data
  statistics of intensity of up crossings of the data
• ENu.simu
  statistics of intensity of up crossings of the simulations
• MDO
  statistics of mean duration over a level
• MDU
  statistics of mean duration under a level

Examples

data(meteo.data)
data = array(meteo.data$temperature,c(31,41,1)) 
k = 40
plot(data[,k,1],typ="l",xlab=("time (days)"),ylab=("temperature (degrees C)"))
T = dim(data)[1]
N.samples = dim(data)[2]
d = dim(data)[3]
# Fit Homogeneous MS-AR models
M = 2
order = 1
theta.init = init.theta.MSAR(data,M=M,order=order,label="HH") 
mod.hh = fit.MSAR(data,theta.init,verbose=TRUE,MaxIter=10)
# Simulation
yT = 31
Bsim = 10
Ksim = Bsim*N.samples
Y0 = array(data[1:2,sample(1:dim(data)[2],Ksim,replace=T),],c(2,Ksim,1))
Y.sim = simule.nh.MSAR(mod.hh$theta,Y0 = Y0,T,N.samples = Ksim) 
valid_all(data,Y.sim$Y)