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I'm reading through some documentation on timeseries.

The first-order difference for timeseries is given as:

$y'_{t} = y_{t} - y_{t-1}$

The second-order difference for timeseries is given as:

$y''_{t} = y_{t} - 2y_{t - 1} + y_{t - 2}$

How is the second-order equation derived? I was thinking that it should be the following but this doesn't make sense ...

$y''_{t} = y'_{t} - y_{t-2} = (y_{t} - y_{t-1}) - y_{t-2}$

Simple answers preferred over complex answers.

Chris Snow
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1 Answers1

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The second difference is defined as the difference of the first difference. That is, it is $$y'_t - y'_{t-1} = (y_t - y_{t-1}) - (y_{t-1}-y_{t-2}) = y_t - 2y_{t-1} + y_{t-2}.$$

Minus One-Twelfth
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