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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. |
