TE between randomly generated time series

[aurelio05]

Dear David!

I tried computing the transfer entropy between two random numbers. To my surprise, causation is detected. In line with this, I have some questions:
Does the length of the sample/data size affects the results? If so, what is then the ideal data length?
Why is causation detected between random variables? I created a random number x ranging from 18 to 32 and y ranging from -3 to 3. I used sample length of 100, 200 and 300. See attachment.
Let me know your thoughts about this.

I would really appreciate any response from you.

Thank you so much and apologies for bugging you.

Kind regards,
Aurelio

[DavZim]

Hi Aurelio,
can you rerun the examples with some larger Ns, ie in the thousands?
If we have only a few observations with a large number of bins we are more likely to see "false positives" when it comes to the p-values.

[aurelio05]

Dear David,
Indeed larger Ns (in thousands) reduces the false positives. I am just wondering, what if your data size is less than a thousand? So one way is to reduce the number of bins, say 3-4. But chances are, you will still get false positives. Any thoughts on this? Thanks!