#
# 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_01.R')
source('numerically_evaluate_xt_ARMA_01.R')
source('newton_fit_ARMA_01.R')

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

theta10 = 0.5

# Compute [a_t] under this initial value of theta:
res0 = uncond_sum_of_squares_ARMA_01(theta10,w_t)
a_t_0 = res0[[3]]

# Compute the (negative) derivative or x_t for this value of theta:
x_t = numerically_evaluate_xt_ARMA_01(theta10,a_t_0,w_t)

print("The negative derivative or x_t is given by...")
print(x_t[10:30])

# Use newton iterations to get an estimate of theta:
print("Newton iterations (and final estimates) look like...")
newton_fit_ARMA_01(w_t,0.5,T)