You should probably focus on results that exceed your -0.1 and 0.1 threshold. The interpretation, I believe, should reveal why sometimes the threshold is exceeded, while values within the threshold are probably non-significant. Good luck!

Hi Vasker,

First of all, it should always be kept in mind that correlation, by definition, quantifies the linear dependance (co-variability) of any two given variables which DOES NOT imply that there is a causal relationship between them.

Having said that, in this plot you have correlation coefficient (r) values computed between rainfall and SOI, along with horizontal coloured lines which could be indicating some sort of significance values (is it the case? otherwise, an objective measure of significance needs to be assessed in order to extract those values that are indeed significant). r values at lag zero give a measurement of the co-variability between the two variables "at the same time", while considering different lags show how a given variability in one variable could have an effect on the other variable some months later or before.

Negative or positive lags are defined depending on how you have considered the variables, that is, which is "variable 1" and which is "variable 2" to be correlated. In this case, a cross-correlation at lag -3 could mean that you are correlating variability in precipitation at a given month against variability in SOI three months earlier. This would mean that you are contrasting Jan 1990 with Oct 1989, Feb 1990 with Nov 1989, Mar 1990 with Dec 1989, and so on. Naturally, the opposite holds for cross-correlation values at positive lags.

Hope that helps!

Ramiro Saurral Thank you. I think I get it to some extent. Those two horizontal lines represents 5% significance level. My variable 1 is Rainfall (monthly) and variable 2 is SOI (monthly). so I tried to lag varraible1 (i.e. monthly rainfall )by 12 lags with variable 2 (i.e. monthly SOI). So does the interpretation still remains same as you have given above?

Another concern is that, is it okay for me to correlate direct monthly rainfall to SOI (which I have actually done)? Shouldn't I reduce the monthly rainfall to some rainfall anomaly index or detrended series before I correlate with SOI? Please help me with this question.

Yes, you should definitely consider anomalies instead of full values, given that keeping the values as they are could lead to artifically enhanced correlation due to, for example, the annual cycle of the variables (if any).

My suggestion is to compute anomalies on both variables and then recompute the cross-correlations. It could also be interesting to undetrend the variables as well.