|
r-squared
Description
The Linear Regression method provides several useful outputs for
technical analysts, including the r-squared. R-squared shows the
strength of trend. The more closely prices move in a linear
relationship with the passing of time, the stronger the trend.
Interpretation
r-squared values show the percentage of movement that can be
explained by linear regression. For example, if the r-squared value
over 20 days is at 70%, this means that 70% of the movement of the
security is explained by linear regression. The other 30% is
unexplained random noise.
It is helpful to consider r-squared in relation to Slope. While
Slope gives you the general direction of the trend (positive or
negative), r-squared gives you the strength of the trend. A high
r-squared value can be associated with a high positive or negative
Slope.
Although it is useful to know the r-squared value, ideally, you
should use r-squared in tandem with Slope. High r-squared values
accompanied by a small Slope may not interest short term traders.
However, high r-squared values accompanied by a large Slope value
may be of huge interest to traders.
One of the most useful way to use r-squared is as a confirming
indicator. Momentum based indicators (e.g., Stochastics, RSI, CCI,
etc.) and moving average systems require a confirmation of trend in
order to be consistently effective. R-squared provides a means of
quantifying the “trendiness” of prices. If r-squared is above its
critical value and heading up, you can be 95% confident that a
strong trend is present.
When using momentum based indicators, only trade overbought/oversold
levels if you have determined that prices are trendless or weakening
(i.e., a low or lowering r-squared value). Because in a strong
trending market, prices can remain overbought or oversold for
extended periods. Therefore, you may want to reconsider trading on
strict overbought/oversold levels used by many indicators. An
“overbought” market can remain overbought for extended periods in a
trending market. However, a signal generated by a moving average
crossover system may be worth following, since these systems work
best in strong trending markets.
To determine if the trend is statistically significant for a given
x-period linear regression line, plot the r-squared indicator and
refer to the following table. This table shows the values of
r-squared required for a 95% confidence level at various time
periods. If the r-squared value is less than the critical values
shown, you should assume that prices show no statistically
significant trend.
You may even consider opening a short-term position opposite the
prevailing trend when you observe r-squared rounding off at extreme
levels. For example, if the slope is positive and r-squared is above
0.80 and begins to turn down, you may consider selling or opening a
short position.
There are numerous ways to use the linear regression outputs of
r-squared and Slope in trading systems. For more detailed coverage,
refer to the book The New Technical Trader by Tushar Chande
and Stanley Kroll.
|
