Z-Statistic

by: Bill Zimmer Monday, September 16th, 2013 at 9:42 am

You are experiencing a series of drawdowns in your trading.  Is this indicative of a buying opportunity or indicative of a system that has stopped working?  Two traders might look at the same data and come to either decision.

But ask yourself, isn’t this the same question as whether a particular market is trending or in a trading range?  In a trending market rising prices are followed by rising prices, with a working system higher equity begets even higher equity. Likewise declining prices are followed by declining prices. In a broken or no-longer working system declining equity begets even lower equity.  In a trend-less or trading range environment rising prices are followed by falling prices and falling prices are followed by rising prices.

A Trend following trading system is profitable in a trending market, stays with the trend and exits or reverses when the trend changes.  A trading range or mean reversion trading system takes positions opposite the trend.

There are statistical tests that help identify whether a market is trending or not. A runs test takes a time series and assigns each data point a + if it is higher that the previous data point and a – if it is lower or unchanged.  A run is a sequence of any number of data points that have the same sign.  The data points can be of any length, hourly, daily, weekly.  Closed trades is another possibility when looking at whether our system is failing or just going through normal drawdowns.

  • The number of points N =44.
  • The number of Wins (+) W=7.
  • The number of losses (-) L=7.
  • The number of Runs R =8.

Where X = 2*W*L = 2*7*7=98

  • If Z is negative, there is a positive serial dependency, which implies trending, and fewer but longer streaks.
  • If Z is positive, there is a negatve serial dependency, which implies trading range, and more but shorter streaks.
  • The magnitude of Z indicates how far from the expected random value this data series is.

One can use this to determine if a market, stock, or ETF is trending or not.  By keeping good records on your trading system this can also be an affective way to determine if your system is no longer working (it happens), or just in a corrective phase.

* Information gathered from Quantitative Trading Systems by Dr. Howard B. Bandy.