Prediction seems to erroneously use knowledge of the value being predicted

[andrew-edwards]

I'm using the notation from Deyle et al.'s (2013, PNAS, 110:6430-6435) Supporting Information. A time series has values X(t), and so for E=2 the lagged space consists of vectors
x(t) = (X(t), X(t-1)).

For target time t*, we are trying to predict the X(t* + 1) value.
By definition, X(t* + 1) is included in
x(t* + 2) = ( X(t* + 2), X(t* + 1) )
and so it seems that we should not be allowed to use x(t* + 2) to predict X(t* + 1).

However, I think that the current rEDM::block_lnlp() function does allow this.

I have forked rEDM and created a new test test_12_block_neighbor.R to demonstrate the issue, see: https://github.com/andrew-edwards/rEDM/tree/andydev (andydev is the branch). The test currently fails, but I think should pass if I am correct and block_lnlp() gets updated (I can't easily see how to do that, sorry). The test code can be stepped through to check the results (just don't run the testthat::test_that line).

I can provide more details if anything is not clear, and happy to discuss anything. I started with test_05_simplex_calculations.R that Hao wrote to test an earlier issue, and adapted that to make the new calculations and the new test. Thanks.

[andrew-edwards]

Hi, anyone have any thoughts on this issue? Thanks.

[ha0ye]

Hi @andrew-edwards,

Sorry, your original message came through while I was traveling, and I forgot to get back to it.

I'm a bit confused about your question:

For target time t*, we are trying to predict the X(t* + 1) value.
By definition, X(t* + 1) is included in
x(t* + 2) = ( X(t* + 2), X(t* + 1) )
and so it seems that we should not be allowed to use x(t* + 2) to predict X(t* + 1).

We don't currently have any checks for this sort of thing in block_lnlp() or simplex() and s_map(). For the latter, a reasonable fix might be to issue a warning when tp = 0, and so the unlagged time series is included as a coordinate in predicting itself.

In the case of block_lnlp(), adding the same warning (but there also needing to check whether the selected column as a predictor is also the column set as the target).

Is this summary about right?