%%  This modification is for the case when we first fit a trend 
%%  --here, quadratic,
%%  and then fit the seasonal. We also attempt to find autocorrelation

X = load('./data/mauna-loa.csv');

co2 = X(:,2);
co2 = co2(11:length(co2));   % throw out first 10 months 

n = length(co2);  % number of obs 

years = 50;

M = 6;

w = ones(2*M+1,1)/12;
w(1) = 1/24;
w(13) = 1/24;

m = co2*0 + 300;
for t = (M + 1):(n-M),
   m(t) = sum( co2((t-M):(t+M)).*w); 
  
end

plot(co2)
  hold on
plot(m,'r');