Hi Gersh,
To calculate linear regression channels, you first calculate the linear regression line of a a distribution of points, in this case closing prices. This is normally done using the "least squares" method. The result is a trendline that describes, within pre-defined time limits (this is important!!), the average price during that time as a function of time. It is also called a line of best fit, or best-fit line.
The best-fit trendline has certain assumptions about the underlying distribution, but in most cases these assumptions are valid. If there are monster gaps up or down, or a sudden shift in trend, or even a more gradual shift in trend, then these assumptions may be violated to a degree that can lead to regression lines that are misleading.
In any case, once the regression line is established, then it is a simple matter to calculate the limits. These are usually defined as 2 standard deviations on either side of the regression line. Since in any Gaussian or near-Guassian distribution 2 standard deviations plus and minus the mean of the distribution encompasses 95% of the points within that distribution, then the two regression channel "rails" similarly define 95% of the points within the channel.
Depending on the nature of the underlying distribution, this may appear to include all the points, or some of the points may occasionally lie outside the rails. If too many points are outliers or "inliers", then this should serve as warning that there is something about the underlying distribution that makes the distribution poorly suited to this type of analysis. In other words, the characteristics or the distribution have sufficiently violated some of the basic assumptions to compromise the validity of the regression lines in the first place, and hence will tend to dilute the predictive power. This happens increasingly as the distribution of prices in question becomes less Gaussian, for example is prices are sharply skewed in one direction or another.
So, assuming the best-fit line is a tight fit, then the regression channel essentially defines a range of prices that will include 95% of prices going forward, so long as fundamental features of the distribution do not change markedly.
But beyond that, the regression line describes the line that data points within the distribution tend to regress towards. So, the further prices deviate above or below the regression line, the stronger the tendency for the regression line to "pull" prices back towards it.
This is something like the zero line in the MACD histograms, which are strongly influenced by regressive tendencies of the MACD.
Using the rails as potential buy and sell points is a little better than using BB rails in the same way, in my opinion. The reason is because the regression channel rails are not pushed around by price movement (but remember, if there are significant numbers of points outside the rails, that is a warning that using regression channels may not be valid in the case in question). On the other hand, the tendency of prices to periodically push against the BBs can be a very useful feature, and can often be anticipated from the width of the BBs as a function of time.
So, I tend to use both regression channels and BBs, because I think they can complement one another, or corroborate one another. They can also provide subtle but sometimes very significant pieces of information that are uniquely found in one method but not the other, so using both gives me a more complete picture of things.
NOTE: It can make a huge difference where you set the time limits of your regression channel. This must be considered carefully. I like to define the beginning of the current trend in question, then set the beginning of the regression channel to coincide with that.
If you take a stock that has suddenly shifted trends, you will see what a difference this can make. For example, look at the weekly chart of AMD.
Here is what it looks like if you set the regression channel to include the entire 52 weeks in the 1-year chart:
139.142.147.218
Here is the weekly chart of AMD if you set the regression channel time limits to the point at the "peak", just before the monster gap down:
139.142.147.218
Now if you set the beginning of the regression channel to the point at the bottom of the gap, you get a much different picture:
139.142.147.218
These regression channels define distict distributions of price ranges that roughly correspond to radically different trends !!!
So depending on how you are trading AMD in terms of time frame of the trend (short term, medium term, or long term), you must tailor the regression channels to the intended purpose.
In the case of AMD, you can easily see that there was a change in long-term trend defined by the market top and subsequent failure at the 200 sma that coincided with the monster gap down. Now, the long-term trend is not up, but down. So using the 52 week regression channel will not be useful because you have two conflicting trends within that regression channel. Instead, you have to select out the points that are inconsistent with the current long-term trend. So the regression channel I think most relevant for that purpose is the one that begins at the market top:
So in my view, improper use of the regression channels could suggest that AMD is a pretty good long position:
139.142.147.218
But proper use of the regression channels indicates precisely the opposite:
139.142.147.218
So, this is one reason I am short AMD (long term).
Hope this helps,
T |
