Hi, I hope I'm posting this in an appropriate place. It's not exactly linear regression.

If you have a seasonal moving average model like \(\displaystyle ARIMA(0,0,0)(0,0,1)_{12}\), and you want to find the expectation of \(\displaystyle y_t\), then you just use the fact that expectation is a linear operator and that the expected value of any error term is zero. However if you have a seasonal auto-regressive model like \(\displaystyle ARIMA(0,0,0)(2,0,0)_{12}\) for example, it will look like \(\displaystyle y_t=cy_{t-24} + \varepsilon_t\). So trying to compute \(\displaystyle E(y_t),\) you get \(\displaystyle E(y_t)=cE(y_{t-12})+\displaystyle E(\varepsilon_t)=cE(y_{t-12})\) but where do you go from there?

If you have a seasonal moving average model like \(\displaystyle ARIMA(0,0,0)(0,0,1)_{12}\), and you want to find the expectation of \(\displaystyle y_t\), then you just use the fact that expectation is a linear operator and that the expected value of any error term is zero. However if you have a seasonal auto-regressive model like \(\displaystyle ARIMA(0,0,0)(2,0,0)_{12}\) for example, it will look like \(\displaystyle y_t=cy_{t-24} + \varepsilon_t\). So trying to compute \(\displaystyle E(y_t),\) you get \(\displaystyle E(y_t)=cE(y_{t-12})+\displaystyle E(\varepsilon_t)=cE(y_{t-12})\) but where do you go from there?

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