IMA_minimization = function(w_t,deltaL=0.05){
#
# Inputs:
#   w_t : the input time series
#   deltaL : the width in spacing between samples of lambda_{-1}, lambda_0, lambda_1.
#   smaller sampling widths take more time to perform searches for the global minimum.
# 
# 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.
# 
#-----

source('uncond_sum_of_squares_ARMA_03.R')

# The grid we will search over: 
lambda1m = seq(0,1.4,by=deltaL)
lambda0 = seq(0,1.4,by=deltaL)
lambda1 = seq(0,1.4,by=deltaL)

# The *unconditional* sum of squares function S_(lambda1m,lambda0,lambda1)
#
min_s_value = Inf 
min_lambda1m_spot = NaN
min_lambda0_spot = NaN
min_lambda1_spot = NaN
for( lim in 1:length(lambda1m) ){
  for( li0 in 1:length(lambda0) ){
    for( li1 in 1:length(lambda1) ){
      ss = uncond_sum_of_squares_ARMA_03(lambda1m[lim],lambda0[li0],lambda1[li1],w_t)
      if( ss[[1]] < min_s_value ){
        #print(sprintf("NEW MIN: lambda1m = %10.6f lambda0 = %10.6f; lambda1 = %10.6f; S= %10.6f",lambda1m[lim],lambda0[li0],lambda1[li1],ss[[1]]))
        min_lambda1m_spot = lim
        min_lambda0_spot = li0
        min_lambda1_spot = li1
        min_s_value = ss[[1]]
      }
    }    
  }
}
list( c(lambda1m[min_lambda1m_spot],lambda0[min_lambda0_spot],lambda1[min_lambda1_spot],min_s_value) )

}