Irregularly Sampled Time-Series

As I was researching options for analysis of irregularly sampled time-series data for the bitcrawl project I started to wonder whether it even made sense to think of the data in terms of a time series. All the articles I read come from the viewpoint of analyzing a physical system, looking for things like the power spectral density or wavelet functions, which can help pull out the underlying character of a linear dynamic system hidden beneath noise. But there is no such system in the financial markets. When traders talk about high frequency trading with bandwidths exceeding 1 MHz, that's when you realize that the dynamics are those of computer algorithms and complex systems, not physical systems. It's like watching the lottery ping pong balls rattle around in a glass sphere. It's totally meaningless. Thermodynamics, with bandwidths in millihertz is the only reasonable physical system for modeling that kind of complexity. I don't want to compete with the ping pong ball catchers that have to build ever faster data centers and fiber networks to keep up with the speeding bullets. Human social dynamics take over in the millihertz range. And when you start talking hours and days or even months between trades (as for me) you need a more all-encompassing metric that reaches into the really low frequencies for which you have almost no data. It's like my Low Frequency Impedance measurement algorithm invented 20 years ago--you can extrapolate a single point on a spectrogram from as little as 1/3 of a sinusoidal period.

But markets aren't physical systems that can be probed with pure sinusoid inputs. Instead, it seems to me, your best bet is to think in terms of volumetric spans rather than time spans. Or even better, just in terms of transaction counts. What matters is how far the price moved between trades, not between days, hours or microseconds. How many different people or groups of people or computer algorithms decided to adjust their price and by how much? That's a fair gage of the "temperature" or "pressure" of the thermodynamics of the market. Of course with electronic exchanges facilitating HFT, these independent actors are getting parsed into the tiniest little chunks. So volumetric measures may be even better. That helps get over the fractal nature of the markets. In the end, even a fractal has a volume, as least it's projection in 3-space does. Hopefully the same concept makes sense for the markets, because that's the path we're crawling down with bitcrawl.

But time is money, so eventually we'll have to do the conversion back to real time, based on some average trade frequency or volume rate for a given instrument. But my guess is we'll discover a lot of hidden dynamics lurking in volumetric and transaction-count space. I hope I can find a market to give me this level of detail.Bitfloor is all I've got right now, without succumbing to the price-gouging of Bloomberg or other financial services, or public exchanges.