Regarding the linked "paper"(which is referred to as "informal paper" on INRIA - meaning nobody who has an idea about this stuff reviewed it!):
It seems they ignore all issues with hand-waving (the talk of nonstandard analysis is just the excuse, the authors' (mis-)understanding of nonstandard analysis seems very vague). They basically approximate the signal (eod prices for some example asset) with a third or fifth order linear recurrence relation, the parameters of which are smoothly adapted to the signal.
Not surprisingly the result looks similar to a very short-term moving average and it has about as much predictive power.. There are empirical studies about which heuristic (e.g. moving averages) performs how well, and when - google helps find them. The one discussed in that paper hasn't been studied to my knowledge, but feel free to try it yourself - if it works you'll make loads of cash!
But think about that: If it is that simple to predict what happens next, wouldn't the big players like GoldmanSachs be exploiting that to the maximum already? There is a maximum, btw: The more money is exploiting the same inefficiency (like for example predictability), the weaker it gets. There are notable exceptions, e.g. bubbles, but they have a lot more to do with behavior than time series.
And of course the EMH is overly simplistic, but it's not as if the mathematicians at financial institutions are complete idiots! This whole idea of a "longstanding quarrel in quantitative finance whether there are trends or not" is pretty much nonsense - of course there are trends, even the simplest models allow for trends - there is no controversy. You just have to know when to make which simplifying assumption to get the best result.
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