set echo off
set messages off

# Illustration of spurious regression
nulldata 100
# define the data as time series for graphing
setobs 1 1 --special-time-series

scalar type1a = 0
scalar type1b = 0
scalar N = 1000

matrix R2 = zeros(N,2)
matrix tmat = zeros(N,2)

loop i=1..N --quiet
    series e = normal()
    series y = cum(e)
    series a = normal()
    series x = cum(a)
    # A: regression of normal y on normal x
    ols e 0 a --quiet
    scalar tstat = $coeff[2]/$stderr[2]
    type1a += (abs(tstat) > 2.0)
    R2[i,1] = $rsq
    tmat[i,1] = tstat
    # B: regression of unit-root y on unit-root x
    ols y 0 x --quiet
    scalar tstat = $coeff[2]/$stderr[2]
    type1b += (abs(tstat) > 1.96)
    R2[i,2] = $rsq
    tmat[i,2] = tstat
endloop

printf "A: Instances of |t| > 1.96: %.1f percent\n", 100*type1a/N
printf "B: Instances of |t| > 1.96: %.1f percent\n", 100*type1b/N