Fractals and The Importance of Time Frame Diversification

Investors and traders often take a one-dimensional view of time frames in the stock market. The media pundits often refer to the fact that it is a “bull” or “bear” market as if there was only one time frame required to make such an assertion. Contrast that with the fact that both traders and investors operate on widely varying time frames from minutes to years, and that a person’s preferred time frame can change with the market itself. People often talk about the 200-day moving average or a 10-month moving average as if the market must operate and will continue to operate on such cyclical frequencies. And let us put aside for now the obvious “observer effects” that cause seminal shifts in historically validated behavior. The success of any moving average strategy is often just an artifact of the market environment itself rather than any special pattern in market behavior. In roaring bull markets, most moving average strategies that are less than 1 year in length will look silly in relation to buy and hold. In a falling market, most moving average strategies less than 1 year will look smart.

Even within such periods such as roaring bull markets of the 1990s that were less kind to long-term moving average systems, there were highly predictable short-term and even intra-day trends. The reverse has been true of the last several years, where short-term trends and intra-day trends have either been mean-reverting or very noisy and difficult to trade. The problem lies with our tendency to think of the market as operating in one particular time frame. But this is dangerous not just for trading, but also for generating any statistical input for factor models or optimization as well. Financial time series data is so noisy that the risk of ignoring multiple time frame information is even more significant.

The reality of time series data is that it shares much in common with fractals that can appear very different as you look at smaller or larger pictures. A fractal chart can have near infinite total length which is a bounded only by the divisibility of time frames for trading. A trend is therefore in the eye of the observer: if I consider the coastline of Britain to represent a fractal chart, my impression of the shape of Britain depends on whether I look up close or from afar. Assuming that there are several thousand scales from which I could observe the coastline, if I was placed randomly in only one scale (or time frame) I could mistakenly conclude that the next bend would be to the right versus to the left by extrapolating from my own narrow point of view. The probability that I would make a correct guess would be nearly random. However, if I could place different observers to looks dozens of scales at once and simultaneously, with proper co-ordination I could make an informed judgement that would be better than random. If those different scales contain variable degrees of noise, then different scales will be more informative than others. The meta-optimized integration of scale information will then further improve my odds of success especially if scale noise in non-stationary.

If this example seems a touch philosophical, I would urge you to think deeper and consider the implications of what this means for trading and investing. At the very least to me it implies that we must all trade multiple time frames, and be prepared to favor some more than others differently at different times. It also means that statistical inputs should contain numerous time frames for measurement spanning from high-frequency to daily, two-day, weekly etc. If we make no a priori assumptions about time frame preference then we should set up measurements like returns,volatility, and correlations for example to be parameterless and straddle a wide range of possibilities to avoid overfitting.