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1 vote

Estimating an ARMAX model using an I(2) exogenous variable

Let us call your endogenous I(1) variable $Y_t$ and the exogenous I(2) variable $X_t$. Your approach is fine unless $Y_t$ and $\Delta X_t$ are cointegrated. In the latter case, differencing $Y_t$ once ...
Richard Hardy's user avatar
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
  • 73
2 votes

Brockwell/Davis seem to say more persistence implies better predictability---do I have a counterexample?

As things stand, I cannot see how the prediction MSE for any process that regularly has an error term $\epsilon_t$ with variance $\sigma^2$ coming in, independently of what happened before, can ever ...
Christian Hennig's user avatar
0 votes

Are stationary processes non-predictable, and non-stationary ones predictable?

Here is a possible angle on this (cf. Brockwell/Davis, p40): The best linear predictor $l(Y_{T})=aY_{T}+b$ for a stationary time series $Y_{T+h}$ based on $Y_{T}$ minimizes $E[Y_{T+h}-aY_T-b]^2$ and ...
Christoph Hanck's user avatar

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