I have been looking at more of these ME on signals and the conclusion I am coming to is that the frequency content is mostly concentrated at the high end of the spectrum. Of course, that is where most of the noise is, so it is difficult to tell information from noise... Still, if the signal is mean reverting which it appears to be from the auto-correlation function, that means buying the dips and selling the spikes, i.e., fading noise traders (note, this is not a stock price it is an abstract signal representing complex option volatility model so don't extrapolate this "rule" to that to the underlying) should be profitable.
What you say makes some sense. However, you have to be very careful about what you are exactly interpreting. Keep in mind that when you de-trended (differenced) to get the stationary signal, you just removed an enormous contributor to the actual signal, which is the low frequency component (you effectively high pass filtered the content). Conceptually, your basic conclusion is what mean reversion is all about; so I have no disagreement there.
True, but I don't have to throw out the low frequency time signal. I should be able to hand a model both inputs, and in theory anyway it should be able to come up with trading rules based on the time domain and frequency domain inputs. I am curious, do you just have a passing interest in this stuff (theoretical), or have you looked at it extensively and have run trading systems through neural nets, etc?
Without divulging much, I have more than a passing interest in these concepts. Let's just say I'm very knowledgeable about them. With regards to whether I've investigated the concepts in trading;a resounding yes. Although, like any other concept there are many pitfalls depending on how you interpret them and what you use them for. I've said it a million times before and I'll say it once again, It's not the higher math that is difficult, it is how you set up the problem to be solved that is difficult. You can pick up any of eldher's books to get some ideas of the concepts applied to markets ( I'll let you judge whether or not his systems are useful).
Thanks. Yeah, I have known of Ehlers work for at least 15 years. I have always thought he took a good approach. Canned software for the most part has always been a complete disappointment to me. I have a couple of his books, and at one time early in my career I tried to use some of his tools within EasyLanguage TradeStation. I couldn't get any of this stuff to give me an edge back then. This could be say more about me than his stuff. Also, I was far less sophisticated back then than I am now....I also looked at the Jurik stuff and couldn't make any of it work. Today I have more of an idea of how to use these tools, but even now their use to me are more to direct research, than to actually use it in the final product.