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How is mean-reversion behavior captured within ARIMA models? What coefficients determine speed of mean-reversion?

Let $\hat x_t=E(x_t\mid x_1,\dots,x_p)$ denote the expectation of $x_t$ conditional $x_1,x_2,\dots,x_p$. I leave it as an exercise to show that $\hat x_t$, for $t>p+q$, satisfies the homogeneous ...
Jarle Tufto's user avatar
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4 votes

How is mean-reversion behavior captured within ARIMA models? What coefficients determine speed of mean-reversion?

Assuming the AR(p) $$ X_t = \mu + \phi_1 X_{t-1} + \phi_2 X_{t-2} + \ldots + \phi_{p} X _{t-p} + \epsilon_t.$$ is specified correctly, (i.e: invertible and $y_t$ is stationary ), then the long term ...
mlofton's user avatar
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1 vote

Regarding explosive AR processes and stationarity

changing an explosive AR process to be in a future dependent form is pointless, real life does not operate that way Is there a reason we don't consider the case of $|\phi|>1$? Is it also because &...
ABCBAA's user avatar
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