cond_sum_of_squares_ARMA_01 = function(theta,w_t){
#
# Given a time series of differences in w_t this function computes the conditional sum of squares
# for an AR(0) MA(1) model conditioned on the given value of theta and with a_0 = 0.
#
# 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.
# 
#-----

# Compute the sequence of a_{t} (forward) using the recursion a_t = w_t + theta * a_{t-1} and starting with a_0 = 0 :
#
a_t = rep(0,length(w_t))
for( ti in 1:length(w_t) ){
  if( ti==1 ){
    a_t[ti] = w_t[ti] 
  }else{
    a_t[ti] = w_t[ti] + theta * a_t[ti-1]
  }
}

# Compute the expressions S_star:
#
return( sum(a_t^2) )

}