# Correlation of two events over time

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:

1. I'd like to see if Event_1 and Event_2 over time.

2. 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.

• How could you look at whether events 1 and 2 are correlated within each year (rather than over years) if both are only observed once? – Patrick Coulombe Oct 31 '17 at 17:41
• What are the numbers? Are they the frequencies of the events? It would be very helpful if you told us what the events actually are. – Zahava Kor Oct 31 '17 at 18:49
• @PatrickCoulombe I edited OP as that bit was ill-posed. I wanted to mean that if the two events are correlated over time in some sort of trend, does this only hold for "over time" as a whole or also for each year-point? (Not sure if this answers your question). – Enoch R. Nov 4 '17 at 10:27
• @ZahavaKor They are frequencies, yes. Just a figure of how many times that event happened in that year. – Enoch R. Nov 4 '17 at 10:28

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.

• Thanks, this sounds like a promising point to get started with time-series analysis. Do you happen to know of any reading you'd recommend to get started with these issues? A primer-like text would be amazing. – Enoch R. Nov 4 '17 at 10:33
• There are some solid texts from the series for statistics for social scientists. I enjoy those. But that aside, there are some really solid videos on youtube. – JWH2006 Nov 6 '17 at 13:17