rndseed 12345
!nrep=10000
!n=30    ' Net sample size  is 20 less than this value, as the first 20 obs. are discarded
series y
series s
series ts
series dfs
series prod
series abbs
series dumm
scalar rho=1
scalar rhohat
vector(!nrep) t
vector(!nrep) df

for !I =1 to !nrep
smpl 1 !n
y=0
s=1
smpl 2 !n
y=rho*y(-1)+@rnorm
smpl if y(-1)<0
s=-1
smpl 21  !n              ' Discard the first 20 observations
prod=s*y
abbs=@abs(y(-1))
rhohat=@sum(prod)/@sum(abbs)   ' See So & Shin, p.166
equation eq1.ls  y  y(-1)      ' Use OLS to estimate sigma - see So & Shin p.167
t(!i)=(rhohat-rho) / (@sqrt(!n-20)*@se / @sum(abbs))   ' This is the Cauchy t-statistic
df(!i) = (@coefs(1) - rho) / @stderrs(1)  ' Construct the usual DF test statistic
next

smpl 1 !nrep
mtos(t,ts)
mtos(df,dfs)
dumm=(ts < -1.645)   ' Assume a 5% nominal significance level
scalar size=@sum(dumm) / !nrep  ' Compute the empirical size of the Cauchy  test
show size
smpl 1 !nrep
show ts
hist ts
show ts dfs