#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

gen_auto_correlated_data = function(){ 
  y1 = rnorm(51)
  y = y1[-1] + y1[-51] # y1[-1] drops the first point; y1[-51] drops the last point i.e. y[n] = y1[n-1] + y1[n] 
}

n_sims = 25
av = numeric(n_sims)
v  = numeric(n_sims)
for( n in 1:n_sims ){
  X = gen_auto_correlated_data()
  av[n] = mean( X )
  v[n]  = var( X )
}
print( var(av) )
print( mean(v) )
print( var(v) )