Has anyone tried using Fractal properties for testing?

[Qsquare]

Hello all,

I have seen a few interesting posts here and wanted to add some input to discussions. Now the following is a little off the wall; granted, but I was curious. A few posters have discussed Mandelbrot, and one of his key assertions is that fractals (of which markets mirror) tend to be statistically self-similar at all scales.
** edit. I should clarify. He actually said they were not self-similar at all scales,
but self-affine. Slight distinction on scaling.

That being the case, has anyone thought about using much higher sampled data (say 1 min) as a proxy for the lower frequency data (daily, etc)? I know from stylized facts, that certain higher freq. data has certain properties you wouldn't see (such as greater neg. serial correlation, for example). Also, sampling too high and asynchronously (say tick data) would seem to have far more durational differences than LF data. So that's why I mentioned minutes.
Another condition, would be that it would need to be liquid on all scales (to avoid some of the duration/gap issues).

If anyone buys into this, it might be a potential source of richer data for some instruments that might have less (ETFs for example) history available. If it seems feasible, then one might be able to scale the estimates for parameters and results upwards towards the higher time frame? Even flash crashes mirror black swans on an intraday scale (although the data is likely revised backwards). I honestly haven't done the work, but curious to get some thoughts about it.

Anyways, interested to hear any yaes or naes. Also, there is a fractal generator package in R, which allows you to set scaling parameters, which might be a better simulator for those who like synthetic data that might match markets closer.

..as an example, here is something that for all intents and purposes appears as a daily sample, but is really only yesterdays data on SPY. 1 day of intraday 1min data ~ 1 full yr of daily information.

[drm7]

Finding consistent tradeable patterns/indicators using intraday data would be very profitable, since a) you could trade a system with much less capital (initial risk even for a system with wide stops would be 10-50 ticks instead of 10-50 points for a system using daily data.) Also, the gains for a profitable system would compound very quickly.

However, I think that intraday data has several characteristics that make it difficult to create profitable systems of the kind that TradingBlox is built to discover.

a) Limited hours - Imagine a dataset of daily data that had 20 days of high volatililty followed by 10 days of little volatility and liquidity every month. Even 24 hour markets such as ES or EURUSD have many hours of inactivity (or random activity) every day. This has the effect of breaking up long trends that TF systems need to be effective. If you limit your system to only the most liquid hours, then you have to content with gaps.

b) Sensitivity to events - Look at a 1 min or 5 min chart during a economic release day. You see a huge up/down bar immediately after the release.
There are usually at least one or two "numbers" released every week.

c) Randomness - Many trendfollowers will tell you that, on any given day/week month, markets are unpredictable and random - its the odd freak trend that makes up for the randomness and gives them their "edge." It's hard to string together enough days to produce that monster 30R trade that makes up for the "chop." You might say "just trade counter-trend intraday." A trend-follower would counter that the trend and non-trend days would cancel each other out intraday, leaving you with a break-even system before commissions.

I'm by no means an expert on this, and there are a lot of "quants" out there that have figured out how to make money intraday, and many profitable tape readers/chartists who use discretion. This opinion is solely from my experience looking at intraday data (both from a discretionary and systematic POV.) I'd certainly welcome any further discussion on this topic.

[sluggo]

... one of Mandelbrot's key assertions is that fractals (of which markets mirror) tend to be statistically self-similar at all scales.

... one might be able to scale the estimates for parameters and results upwards towards the higher time frame? ... I honestly haven't done the work, but curious to get some thoughts about it

As you're starting out to do the work, perhaps one of the easier ways to test this key assertion might be: Scale the data and parameters and results downwards towards the lower time frame.

I assume you've already got historical prices on the daily scale -- call this data "1-day bars". Now scale the data downwards to produce "N-day bars". Scale the parameters and results downwards by this same factor of N. Did Mandelbrot's predictions come true? Repeat for a few different values of N.

[Qsquare]

Thanks all,

For whatever reason, I guess my question didn't come out too clearly. Sluggo, your approach makes sense; since if they are 'statistically' self similar, it doesn't really matter which direction you choose (well, ok only to start testing the hypothesis, the observational frequency benefits of data sampling does depend on direction).

Not sure I'd call it validating his 'prediction' so much, as validating his hypothesis. It entails using that assertion to increase the availability of observational data and thus reduce variation (and ideally increase certainty) in more sparse lower frequency (ex, daily) results.

[blueberrycake]

In my experience different timeframes are similar in the sense that prices move up, down and sideways on a chart of any time resolution. However, once you get to the point of actually exploiting a particular price behavior via a trading system, you find that the similarity is often purely superficial, and that prices really aren't fractal.

-bbc

[rgd]

I too have found the same thing. While I read and enjoyed Mandelbrot's book, I find that academics try to force everything into neat, tidy, cleary defined categories. I always say that markets are more about the vagaries of mass psychology, than the discipline of any hard science. Fortunately, at a broad level, the tendencies of mass psychology can be profiled and exploited.