#################################
#  Passeio aleatorio sem e com drift
#################################
n = 2000

# Varios drifts diferentes 
rho  = 1.0
par(mfrow=c(1,3))
for (alpha in c(-0.2,0,0.2)){
  e = rnorm(n,0,2)
  y0      = 0
  y = rep(0,n) 
  y[1] = alpha + rho*y0+e[1]
  for (t in 2:n)  
    y[t] = alpha + rho*y[t-1]+e[t]
  ts.plot(y)
  title(paste("alpha=",alpha," - rho=",rho,sep=""))
}

# Series estacionarias
alpha = 0.5
par(mfrow=c(1,3))
for (rho in c(0.9,0.95,0.99)){
  e = rnorm(n,0,1)
  y0      = 0
  y = rep(0,n)
  y[1] = alpha + rho*y0+e[1]
  for (t in 2:n)
    y[t] = alpha + rho*y[t-1]+e[t]
   ts.plot(y)
   title(paste("alpha=",alpha," - rho=",rho,sep=""))
}



install.packages("fUnitRoots")
library(fUnitRoots)
wants  =  c("fUnitRoots")
has    =  wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])
library(mvtnorm)
library(Hotelling)


fUnitRoots