I have 3 time series variables, let's call them A, B, and C, all yearly counts. However, there is an overlap between them (see picture). I am interested in estimating the coloured part.
When broken down into equations, it would look like this:
(X marks the data I have, Y data I don't have/wish to estimate)
X(A) = Y(A/C) + X(A/B) + X(A/B/C)
X(B) = Y(B/C) + X(A/B) + X(A/B/C)
X(C) = Y(A/C) + Y(B/C) + X(A/B/C)
What am I dealing with seems to be 3 equations with 2 unknowns which can be solved for sure for each year. However, since this is time series data, I would like to use this to forecast specifically Y(A/C).
Any idea about the analysis (or more) that can be used to solve this?
Many thanks for every idea or direction!
Hello Lana Bojanic
Would you please share your query by an example in Excel?
certainly a solution can be found through excel functions.
Hi Lana Bojanic,
You question is hard to answer and requires considerable interpretation (guessing) from you readers. Do you mean that your counting data is counted in three separate spatial areas, where these areas overlap in space? In that case you will have spatial auto-correlation in your data. You could consider googling the term "spatial auto-correlation" in combination with "generalized linear model for counting data". That is, of course, if that's would you intend to do...
Hi Pepijn de Vries
thank you for your time. No, the circles represent three separate time series count variables that overlap.
Hi Lana Bojanic,
It will probably help if you explain your problem a bit more. What do these variables represent? How do they overlap (apparently not in space)? It is hard to give a meaningful answer without more details...
Kind regards,
Pepijn
These variance decomposition-thingies are always brain-twisters. I'm not expert in time series models so this is mostly conceptual input:
The image looks like "I'd like to model the covariance between A and C that is not common with B". Set up three vector autoregressive models for A, B and C. Regress A on B, then the residuals from this regression on C. It has to be a sequential approach, because the area of overlap between three variables is not defined within a single model (a covariance exists between two variables/parameters, it's undefined between more than two variables).
In a structural equation model it might work nicely within a single step, by explicitly modeling the residual of A and then correlating this with C.
Hi Lana Bojanic
The article below could help you, because you can applied on your data and the results from it could distinguished depending to the what you looking, if i well understand your question
best regard
Article Windowed detrended cross-correlation analysis of synchroniza...
zainy
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