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Probably this is easy to answer, but let me formulate the question: If we have a variable $Y_t$ measured over time and cross-sectionally, and we calculate the change of this variable from $t-1$ to $t$, let's call it $\Delta Y_t$. Next, we want to predict this $\Delta Y_t$ at time $t$ using several predictors (let's call them $a$ and $b$ for simplicity). My question is as follows: Can we use $a$ and $b$ at time $t-1$, or do they need to be measured at $t-2$? I am asking because $\Delta Y_t$ also contains information from period $t-1$ (logically, as it is the change from $t-1$ to $t$), so does that lead to any problems in the regression model?

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Before trying any modeling with time series, it is important to make sure that time-series you have is stationary. In simple words, it means that, if you select random consecutive sample sizes of n from this time-series they will have equal covariances. One considers time series purely stationary if and only if it complies to the following:

  1. Constant mean
  2. Constant variance
  3. Constant covariance between equally sized periods.

Stationarity is one of the assumptions of regression models.

Edit: Formatting

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    $\begingroup$ Stationarity is a simplifying assumption used in many time series models--but not all. (Consider GARCH, for instance.) This misses the point of the question, which concerns the issue of previsibility. $\endgroup$ – whuber Feb 20 '20 at 15:20
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    $\begingroup$ thanks for the reply, but that does not answer my question yet as indicated by @whuber. $\endgroup$ – Talik3233 Feb 20 '20 at 20:14

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