I have data on two events over a 25-year span of time. The data look like (example below):
Year Event_1 Event_2
1990 1000 800
1991 850 750
1992 1050 850
. . .
. . .
And so on and forth. I'd like to see whether Event_1 and Event_2 are correlated. The figures in the example above are simply frequencies of occurrence of both events. I understand Pearson's product-moment correlation coefficient, but I'm not sure whether that's the best strategy for these data.
I've read about cross-correlation in this other post, but I've never done time-series analysis before. Regarding the data:
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I'd like to see if Event_1 and Event_2 over time.
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I suspect that Event_1 might cause Event_2, but it's just a guess (it could well be the opposite).
Any reference to the literature to get me started with this will be very appreciated.
Best Answer
Seems like a regression problem with year.
Event_1 = Event_2 + Year + Event_2*Year
Well I thought I would expand on this a little more with the commentary below.
You care about looking at the correlation between two events with auto-correlation as an issue. For example, event 1 and event 2 might increase, but that might be because they are correlated and it might be due to auto-correlation.
The trick is to control for this within a model.
You can do something like a simple trend model as well: yt−yt−1=f(xt)+ error. Where yt-yt-1 is just the year to year change. f(xt) is the trend for x and then you have error. Same thing as I described with a small difference in notation.
There is one other thing you can do: a logarithmic model. You will then get an idea if they are proportionately changing.