AR(1) process estimate infer, the number of extracted residual term

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mirewuti muhetaer
mirewuti muhetaer 2019-11-19
Hi, all
let us say, we have 10 observation of variable Y and i use the following code:
[ytrend, ycycle]=hpfilter(Y,1600); %create 10 observations for each.
md1=ar(1,0,0);
summarize md1;
esty=estimate(md1,Y);
%accroding to my understanding, it is Y_t=constant+rho*Y_{t-1} + epsion_t;, so there are total 9 regression in the above estimation process, so there will be 9 observation in the corresponding residual term. however, when i run the following code to extract the residuals.
[yres, yv]=infer(esty, ycycle);
% what i get is 10 observation for yres variable.
how could that be possible?.
Thanks.

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