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To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do you want to forecast volatility over one period? Or over 1000 periods? Or higher moments? Do you want to simulate volatility over one period? Or longer? For ...

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A good rule of thumb is to "test" your models by doing forecasts and to choose the best one. Note however that your choice will be based upon the loss function you selected. If you are concerned about outliers you should (for instance) use Median Squared Errors, if you don't you can use Mean Square Errors. In your particular case the Information Criteria ...

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There is no particular issue with your polynomials. However if you really want them to both start with a 1, you can apply a change of variable by defining : $$Y_t = -\frac{1}{4}X_t$$ Then your polynomials $\Phi_y(B)$ and $\Theta(B)$ such that : $$\Phi_y(B)Y_t=\Theta(B)Z_t$$ will both start with a $1$. It ...

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