Positive Autocorrelation and Trend Trading Success.

In his interesting article “The Main Cause of Failure of Some Popular Technical Trading Methods” Michael Harris says:

“Indicator based trend following and classical chart patterns are two trading methods that were developed in mid 20th century using data from the equity markets mainly and worked well during an extended period of time in those markets due to the presence of autocorrelation. After 1998 things got harder because serial correlation in equity indices decreased due to arbitrage and by 2007 it was mostly gone rendering these methods largely ineffective.

On the above daily chart of S&P 500 from 01/03/1950 to 12/19/2012 the bottom pane is the 1-Lag rolling 120-day autocorrelation of daily arithmetic returns [X(i+1)/X(i) - 1]. It suffices to observe that from 01/1950 to 04/1988 the autocorrelation was very high, especially after 07/1964 and through 04/1988, or for a period of 24 years, with very few and short periods of negative autocorrelation. That was a very good time for technical methods based on trend-following and chart patterns during which some traders might have gotten the impression that these methods are significant although their success was clearly due to the high autocorrelation in the equity markets, i.e. the fact that future prices quite often behaved like past prices. In other markets, like commodity futures and currencies, which started trading in the mid 1970s, these technical methods were later applied and expected to work because they were raised to causation rules by some authors but in reality they failed more often than they worked well and were basically responsible for the high rate of failure of retail traders and even some funds.”

I copied Michael’s instructions and calculated the 1 lag rolling 120 day autocorrelation of the daily arithmetic returns of both on the S&P cash price series and the ratio adjusted futures contract.

I can not attach my charts here but no doubt readers will know where to find them. Firstly they will note the less than perfect correlation between the futures and cash series.

Secondly they will note the far more pronounced downturn in positive autocorrelation for the relevant period of the cash series over the ratio adjusted futures series.

Thirdly I have posted a chart of the equity curve of a simple dual moving average crossover system, 50: 200, trading the ratio adjusted futures contract for the period of its existence from 1982.

My initial conclusion is that the use of serial correlation analysis, or at least the 1 lag rolling 6 month variety, is not of a great deal of value in explaining the success or otherwise of a trend following system. I prefer to define “trendiness” in other ways which I find more helpful.

Hastily tested, written and conceived in my case. No doubt I have missed something and my error will occur to me later.

 

Excellent post, I totally agree. I myself gave up charting and traditional TA several years ago after having tried it for years without success. Today, you definitely need more sophisticated methods like hidden Markov models to predict serially uncorrelated time series.

 

I am certainly no expert on statistics, but doesn't "1-Lag" just mean that the analysis focuses on how the return from day [x+1] related to day [x]?

If that's the case, then the apparent reduction in "1-Lag" autocorrelation could be accommodated by a model that assumes price action from one day to the next is less autocorrelated, but over 2-days (or 3, or whatever) is still autocorrelated.

The underlying mechanism for this could be that high speed automated trading perhaps makes price action more noisy and brownian over the shorter timeframe (1-day) but has less of an effect over a longer timeframe (where fundamentals can still get the upper hand).

 

Yes.

Even in a strong Bull or Bear market, it seems a bit unlikely to me that the daily closing prices of a particular index or instrument would “close” continuously higher or continuously lower day after day. And thus it was not surprising to find that the 1 lag 120 day serial correlation of the price changes in the S& P cash and futures should from time to time show negative serial correlation.

Might it perhaps be more realistic to look at averaging the daily arithmetic returns over, say, a three day period and then look at the 1 lag 120 period serial correlation?

I did that on both price series and perhaps unsurprisingly, autocorrelation remained positive throughout the time periods looked at, never going negative. I wonder if this is perhaps a more realistic view of the markets? Clearly the smoothed results show a far less disturbing and dramatic picture even if they still fail to provide much in the way of explanation for recent trend following woes.

For some reason I have been unable to attach a chart here.

Anthony FJ Garner

 

Thanks for the very interesting article reference. I need to think further as to how to study this better.

 

Can you just put them up on http://imgur.com/ and post the links? Id like to see them, this is an interesting thread.