library(TSA)
library(uroot)
set.seed(1319)
n=50
mu=10
y=rnorm(n=50)+mu
plot(y,type='o')
# choosing between random wlak and zero mean statioonary AR(1)
ADF.test(ts(y),itsd=c(0,0,0),selectlags=list(mode=c(0),Pmax=0))

#choosing between random wlak+linear trend and  stationary AR(1)

ADF.test(ts(y),itsd=c(1,0,0),selectlags=list(mode=c(0),Pmax=0))
trend=time(y)
y=rnorm(n=50)+mu+trend+trend^2
plot(ts(y))
ADF.test(ts(y),itsd=c(1,0,0),selectlags=list(mode=c(0),Pmax=0))

#choose between random walk+trend vs linear trend+stationary AR(1)
ADF.test(ts(y),itsd=c(1,1,0),selectlags=list(mode=c(0),Pmax=0))

#choose between random walk+auadratic trend vs quadratic trend+stationary AR(1)

ADF.test(ts(y),itsd=c(1,1,0),regvar=data.frame(quad=trend^2),selectlags=list(mode=c(0),Pmax=0))

data(oil.price)
?oil.price
plot(oil.price)
hist(oil.price)
BoxCox.ar(oil.price,method='ols')
# log transf may be needed
plot(log(oil.price))
acf(log(oil.price))
ar(diff(log(oil.price)))
ADF.test(log(oil.price),itsd=c(1,1,0),
regvar=data.frame(quad=time(oil.price)^2),selectlags=list(mode=c(1,2),Pmax=2))
# need differencing

plot(diff(log(oil.price)))
acf(diff(log(oil.price)),ci.type='ma')
pacf(diff(log(oil.price)))
eacf(diff(log(oil.price)))
,ci.type='ma')