#
# This code computes the S(lambda_0,lambda_1) for samples of lambda_0 and lambda_1 in an IMA(0,2,2) process 
# and returns the value of lambda_0 and lambda_1 that result in the smallest value.
#
# It would be nice to have this surface plotted as a three dimensional surface.  One should probably 
# do this search over a very coarse grid first and then refine the grid as needed for higher resolution.
# 
# 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_02.R')

lambda0 = seq(0.3,1.5,by=0.01)
lambda1 = seq(0,1.4,by=0.01)

z_t = scan("../../Data/series_b.dat",strip.white=T)
w_t = diff(z_t,differences=2)

# The *unconditional* sum of squares function S_(lambda0,lambda1)
#
min_s_value = Inf 
min_lambda0_spot = NaN
min_lambda1_spot = NaN
for( li0 in 1:length(lambda0) ){
    for( li1 in 1:length(lambda1) ){
      ss = uncond_sum_of_squares_ARMA_02(lambda0[li0],lambda1[li1],w_t)
      if( ss[[1]] < min_s_value ){
          #print(sprintf("NEW MIN: lambda0 = %10.6f; lambda1 = %10.6f; S= %10.6f",lambda0[li0],lambda1[li1],ss[[1]]))
	  min_lambda0_spot = li0
	  min_lambda1_spot = li1
          min_s_value = ss[[1]]
      }
    }    
}
print(sprintf("GLOBAL MIN: lambda0 = %10.6f; lambda1 = %10.6f; S= %10.6f",lambda0[min_lambda0_spot],lambda1[min_lambda1_spot],min_s_value))