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I tried to estimate parameters for the AR(1) and MA(1) models. I got 0.342 for theta and -0.343 for phi (coefficients of AR(1) and MA(1) respectively). The residual ACF for both the models was also the same.

My question is if this is possible? Or that I have an issue with my Matlab code?

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This is quite possible and is to be expected as all AR models can be expressed as MA models . If the ar(1) coefficient is .33333 as is your case it's negated inverse is -1/3 or -.33333. For example an AR(1) model with coefficient .5 generates {1+.5B1 + .25*B2 + .125*B3 + .0625*B4 ,,,,,}

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  • $\begingroup$ Could you please elaborate? Also, I am getting different values for the RMSE. Is this possible? $\endgroup$ – John Crank Mar 24 '17 at 20:40
  • $\begingroup$ i would not expect that $\endgroup$ – IrishStat Mar 24 '17 at 20:48
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So the RMSE must be the same? I think the two RMSE values are very close.

Also, what is the reason for the residual acf being the same?

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