Friday, November 9, 2007

Linear Regression Changes In Trends

The previous post covered using a linear regression line with standard deviation channels. This is helpful to define the trend and to statistically define where the underlying stock or index is in relation to the trend. Below is a three day chart with the same linear regression and standard deviation lines used previously.

MER - Merrill Lynch & Co.(click charts to enlarge)

In this chart the red line running up the center is the linear regression line(377 period). The blue lines are one standard deviation above and below the regression line. The yellow lines represent two standard deviations. Two standard deviations should include 95% of prices. Any price outside this area should be looked at as an extreme in relation to the trend, and should revert back to the mean. If prices stay outside these areas, it signals a change in trend.

As can be seen, one standard deviation acted as support for most prices. Recently prices broke through this area and went straight to the two standard deviation line, where prices paused before breaking strongly lower. This is a great visual picture of the change in the state of affairs for companies with exposure to the sub-prime lending issues. Below is the same chart of Merrill Lynch except it is a daily chart as opposed to the three day chart.

MER - Merrill Lynch & Co.

The daily chart shows more volatile price movement. The three day chart takes some of the noise out of the price movement and smooths the data. The daily chart is helpful for looking for entry points for those who trade more actively.

Below is a chart of Roper Industries Inc. It might look like a pretty boring chart, but is one that has been very profitable.

ROP - Roper Industries Inc.

Applying linear regressions to Exchange Traded Funds can be a helpful tool in identifying leaders. Below are charts of the XLE Energy ETF and the XLB Basic Materials ETF.



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