Forecasting Tomorrow's Trading Day
by Tushar S. Chande, Ph.D.
Using linear regression as a crystal ball for forecasting the market? After all, if you were to be able to
determine tomorrow's high, low and close for trend changes and placement of stop points, it would
simplify your life immeasurably. Can it work? Tushar Chande explains how it can be done.
Wouldn't you trade better It you could "see" the future? A simple linear regression can provide an
objective forecast for the next day's high, low and close. These ingredients are essential for a trading
game plan, which can help you trade more mechanically and less emotionally. Best of all, a regression
forecast oscillator, %F, gives early warning of impending trend changes. The linear regression method is
well known for finding a "best-fit" straight line for a given set of data. The output of the regression are
the slope (m) and constant (c) of the equation
(1)Y = mX + c
Here, m and c are derived from a known set of values of the independent variable X and dependent
variable Y. The relative strength of the linear relationship between X and Y is measured by the
coefficient of determination r2, which is the ratio of the variation explained by the regression line to the
total variation in Y. Here is a table to help interpret the values of r 2, which range from 0 to 1:
The coining of the term "regression" can be attributed to Sir Francis Galton, who observed in the late
1800s that tall fathers appeared to have as a rule short sons, while short fathers appeared to have as a rule
tall sons. Galton suggested that the heights of the sons "regressed" or reverted to the average. Technician
Arthur Merrill also had a good explanation in a recent issue of STOCKS & COMMODITIES, and Patrick
Lafferty recently wrote on an application of multiple regression to gold trading. Virtually all introductory books on statistics have a detailed discussion of the linear regression method.