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

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mirewuti muhetaer 2019-11-19

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https://ww2.mathworks.cn/matlabcentral/answers/491815-ar-1-process-estimate-infer-the-number-of-extracted-residual-term

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.