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This is a bit DSP-related: so if you turn your non-stationary time series into a stationary process, you'll probably see that it is not periodic.. This is an issue for Fourier-based techniques because they are not local in frequency. Now, besides wavelets (some types are causal btw), which other causal techniques can you use? (and ARMA is not it). I tried Empirical Mode Decomposition (HHT), but that's not causal; I tried Intrinsic Time-scale Decomposition: not causal either. Wavelets are pretty old and I would think something better would have been "discovered" by now? Does anyone know of a good causal signal processing technique that deals well with non-periodicity? Thanks!!

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Have you managed to implement some causal versions of wavelets with success? – RockScience Jul 5 '11 at 10:55

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I know only that Jurik's JMA is good causal filter, better than Kalman and Volterra filters, but I don't know for sure what algorithm inside - it's black box. Does anybody know better causal filter?

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Do you of anyone else have more information about this filter? I can only find the author's website and I'm not convinced by it. – Bob Jansen Sep 18 '11 at 12:10
@Bootvis Code for the JMA is available here link – babelproofreader Sep 18 '11 at 19:56
@Bootvis I can recommend you to read this doc for more information:link. – Igor Oct 4 '11 at 13:32
@babelproofreader I've used this code for MT4, but it's not Jurik original. So their quality is little bit different than original ones. – Igor Oct 4 '11 at 13:35
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Wavelets and Kalman filtering.

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Wavelet is not a causal technique. there is a huge boundery effect due to the selection of either "reflection" of "periodic" – RockScience Jul 5 '11 at 10:13
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The issue with wavelets is that you'll have some boundary distortions so be careful when exploiting the results.

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