In a previous publication, we have discussed the common belief that for the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. However, it has been shown on one example, the Euro future contract, that the difference between real financial time series and random walks, as small as it is, is detectable using modern statistical multivariate analysis . This has been achieved using several triggers encoded in a multivariate trading system. Then a non-random content of the financial series can be inferred  . Of course, this is not a general proof  , as we focus on one particular example and the generality of the process can not be claimed. In this letter , we produce a second example on a completely different markets, largely uncorrelated to the Euro future, namely the DAX and Cacao future contracts. The same procedure is followed using a trading system, based on exactly the same ingredients. We show that similar results can be obtained and we conclude that this is an evidence that some invariants, as encoded in our system, have been identified. They provide a kind of quantification of the non-random content of the financial markets explored over a 10 years period of time.
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model is too small to be detected using traditional time series analysis. However, we show in the following that this difference between real financial time series and random walks, as small as it is, is detectable using modern statistical multivariate analysis , with several triggers encoded in trading systems. This kind of analysis are based on methods widely used in nuclear physics, with large samples of data and advanced statistical inference. Considering the movements of the Euro future contract at high frequency, we show that a part of the non-random content of this series can be inferred , namely the trend-following content depending on volatility ranges . Of course, this is not a general proof of statistical inference , as we focus on one particular example and the generality of the process can not be claimed. Therefore , we produce other examples on a completely different markets, largely uncorrelated to the Euro future, namely the DAX and Cacao future contracts. The same procedure is followed using a trading system, based on the same ingredients. We show that similar results can be obtained and we conclude that this is an evidence that some invariants, as encoded in our system, have been identified. They provide a kind of quantification of the non-random content of the financial markets explored over a 10 years period of time.
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