[R] Confusion about cointegration for AR(M) model

[Zhou, Cindy]

I have a question regarding the concept of cointegration. Does the concept of cointegration apply to any model? Or it only applies to OLS? For example, I fit an autoregressive error model , AR(M)

y_t=x_t*â+v_t

v_t=-ö_1*v_(t-1)-...-ö_m*v_(t-m)+å_t

If the ADF tests prove that both dependent variable y and independent variable x are stationary at I(1), and the residuals å_t are stationary at I(0), Can I conclude y and x are cointegrated? The residuals å_t are the prediction errors from the AR(M) model.

I checked the definition of cointegration, it looks like as long as the residuals from OLS are I(0) and both x and y are I(1), then x and y are cointegrated? Do I need to test stationary of the residuals from my AR(M) model in order to prove that x and y are cointegrated?

You help is appreciated.




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