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Hi,

I want to create Bootstrap replicates of an AR(2) Modell in the nonstationary region.

I look at: y_t(restriction)=Beta*delta(y_t-1)+epsilon_t(restriction)

where y_t(restriction)=y_t-alpha(restriction)*y_t-1
alpha=1 implying nonstationarity.
I estimate the equation and save the residuals (makeresid) and draw a lot of replications of them.

Then I turn to the series y_t(bootstrap)=alpha_restriction*y_t-1+Beta_hat*delta(y_t-1)+epsilon_t(restriction).

However, when I investigate this series in terms of stationarity it is indeed stationary, but it should display nonstationarity as alpha_restrction is given by 1.

series y_r=y-y(-1)
eq1.ls y_r d(y(-1))
eq1.makeresid resid_1
next
for !b=1 to !s
series resid_1_{!b}=resid_1
resid_1_{!b}.resample(dropna)
next
Then I create:
series y_b=y(-1)+resid_1_{!b}+d(y(-1))

However, this series displays stationary behavior.

Thank you!