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These are the regression results.

Coefficient in Black, P-Value in Blue and Standard Error in Red. Using these results, can I deduce whether X or Y is the lead or lag variable in the time-series?

wolterskluver
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  • "Lead" usually means *precedes in time" whereas "lag" means "follows in time." That appears to have nothing to do with which variable you use as the lead or lag variable. This comes down to correlation not being causation. – whuber Aug 26 '23 at 15:08
  • @whuber Thank you for your answer. Perhaps, I didn't explain myself well. I'm not interested in causation. Just because one variable follows the other, doesn't necessarily imply causation. My question is limited to deducing which variable shows the change first and which variable follows that variable in reflecting that change. – wolterskluver Aug 26 '23 at 15:21
  • Fair enough -- but the remarks hold nevertheless. Regression does not model temporal sequence. See https://stats.stackexchange.com/a/89039/919. – whuber Aug 26 '23 at 18:05
  • According to Sims, rather than assuming one is the lead and one is the lag, it's best to estimate a bivariate VAR and see what results come out of that. – mlofton Aug 27 '23 at 00:27
  • @mlofton Thank you for proposing a method. Since I'm new to this, could you please elaborate a bit? Also, how do I estimate a bivariate VAR with Y and X in Excel? – wolterskluver Aug 27 '23 at 08:23
  • Hi: A VAR is a regression on steroids where every variable in the system gets regressed on every other variable in the system and the whole system is estimated simultaneously. I'll try to find something on the net that provides an introduction. The bible as far as VARS is probably Lutkepohl's text "Multiple Time Series". Excel won't have anything for estimating a VAR. You would need to use R or Python. – mlofton Aug 27 '23 at 16:37
  • I can't find anything that's very introductory. Also, what to read really depends on background so I'm hesitant to send any links. I suggest getting familiar with R or Python because Excel is only going to take you so far. – mlofton Aug 27 '23 at 16:47

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