An interesting characteristic of time series is autocorrelation — In simple terms, it can be interpreted as memory in markets. Mr. Hurst, a genius British hydrologist came up with the idea when building a dam on river Nile. His work is used today (among other applications) in hedge funds to make money.
A Hurst exponent between 0 and 0.5 indicates anti-persistence (or mean reversion). A Hurst exponent of 0.5 and above indicates persistence in the time series. Persistence is when an up day is followed by an up day or a down day is followed by a down day etc. Anti-persistence is the reverse of it. A value of 0.5 somewhat indicates to a Brownian motion.
Contrary to the belief-system of Random walk on which many pillars of higher finance are built, memory in time series do exist and traders do exploit these. Personally, I believe that models that assume perfect rationality (in human minds) without taking into account the other driving force of ours — emotions, do tend to fail at some level when used as they are. Anyway sorry for dithering and back to this Hurst thingamagic:
I took the S&P 500 index for the last 2 years and ran a moving-Hurst with a 50 day window. Plot is shown below.
What is interesting to note is that the market index has shown persistence for the period in observation in varying degrees. If this were Brownian we should have perhaps seen a somewhat straight line go through 0.5 units. It was also fascinating to note the drastic changes in the exponent itself with time.
Originally published at https://www.linkedin.com.