Compute time delayed dependencies

[pierretoussing]

Another possibility is to look for dependencies over time.

• [x] Write a function that computes the similarity of the reference series to the data shifted by a given amount of time. It takes in a list of integers that indicate how much to shift the data. The output is a plot with the similarity maps for each time shift in one column.

• [x] Look at the nature paper for relevant time shifts (1 month, 3 months, 12 months,...)

[pierretoussing]

In the nature paper, they used the following time shifts:

• 1-2 months

• 2-4 months

• 4-8 months

• 8-16 months

• 16-32 months

• 32-64 months

• 64-128 months

[pawelbielski]

@pierretoussing What is the interpretation of the delay ranges, e.g. 1-2, 2-4? Does it make sense in our case to define delay in that way?

[pierretoussing]

@pawelbielski The delay ranges in the nature paper mean that they used all of this delays for the similarity computation e.g 2-4 means they used the delays 2, 3, and 4 for this one map. This has something to do with the similarity measures they used: Wavelet multi-scale correlation. This measure is designed for such this purpose. Using standard similarity measures, we would then have to define a method to combine the similarity values for 2, 3 and 4 months in order to combine them into one value for the delay range 2-4 months. So using standard similarity measures (and also implementing the approach Peter suggested), we define the time delays as a simple integer and then shift the whole map by this delay. I used 1, 3 and 12 months as delays. It means that the similarity is computed between the actual reference series and the whole map shifted by the respective time delay. I used the mean as fill value to assure the time series still have the same length (to avoid problems with similarity calculations). This delays act as example, I don't know if they are meaningful or if we should use other delays? I thought that the climate scientists would provide us with the delays they want to look at.

[pierretoussing]

Peter suggested that it would be better to drop points in order to keep the length of the time series equal, than filling up with the mean.

• [x] Modify the compute_time_delayed_dependencies so it drops points and does not fill up.