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Today, my professor said that for highly correlated time series, taking the first differentiation is like applying an AR(1) filter.. Unfortunately I a was not able to ask him after the lecture.

I am confused...

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Formula for a differenced time series is

$Y'_{t} = Y_{t}-Y_{t-1}$.

For a stationary time series $Y'_{t}$ should be random noise so $\epsilon_{t}$. So the differenced time series becomes

$\epsilon_{t}$ =$ Y_{t}-Y_{t-1}$.

Rearranging this we get:

$Y_{t}=Y_{t-1}+$ $\epsilon_{t}$

AR(1) is defined as

$Y_{t}=\theta_{1}$$Y_{t-1}$+$\epsilon_{t}$

So as $\theta_{1}$ approaches 1 (highly correlated) applying an AR(1) becomes like a differenced time series.

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