There is a widespread belief in financial markets that trends in prices are arrested at support and resistance levels that are to some degree predictable from the past behaviour of the price series. Here we examine whether ratios of the length and duration of successive price trends in the Dow Jones Industrial Average cluster around round fractions or Fibonacci ratios. We identify turning points by heuristics similar to those used in business cycle analysis, and test for clustering using a block bootstrap procedure. A few significant ratios appear, but no more than would be expected by chance given the large number of tests we conduct
