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<FONT face=Arial color=#0000ff
size=2>
Peter
Gialames
<FONT face=Arial color=#0000ff
size=2>
Here is the text from S&C V.
10:5 (220-224): Forecasting Tomorrow's Trading Day by Tushar S. Chande,
Ph.D.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Using
linear regression as a crystal ball for forecasting the market? After all, if
you were to be able to<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" />
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>determine tomorrow's high, low and close for trend changes and placement
of stop points, it would
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>simplify your life immeasurably. Can it work? Tushar Chande explains how
it can be done.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Wouldn't
you trade better It you could "see" the future? A simple linear regression can
provide an
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">objective
forecast for the next day's high, low and close. These ingredients are essential
for a trading
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">game plan,
which can help you trade more mechanically and less emotionally. Best of all, a
regression
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">forecast
oscillator, %F, gives early warning of impending trend changes. The linear
regression method is
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">well known
for finding a "best-fit" straight line for a given set of data. The output of
the regression are
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">the slope
(m) and constant (c) of the equation
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">(1)Y = mX
+ c
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Here, m
and c are derived from a known set of values of the independent
variable X and dependent
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">variable
Y. The relative strength of the linear relationship between X and Y is measured
by the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>coefficient of determination r 2
, which is the ratio of the variation explained by the
regression line to the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">total
variation in Y. Here is a table to help interpret the values of r <SPAN
style="FONT-SIZE: 10pt">2 , which range from 0 to
1:
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">The
coining of the term "regression" can be attributed to Sir Francis Galton, who
observed in the late
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">1800s that
tall fathers appeared to have as a rule short sons, while short fathers appeared
to have as a rule
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">tall sons.
Galton suggested that the heights of the sons "regressed" or reverted to the
average. Technician
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Arthur
Merrill also had a good explanation in a recent issue of <SPAN
style="FONT-SIZE: 9pt">STOCKS & <SPAN
style="FONT-SIZE: 9pt">COMMODITIES, and Patrick
Lafferty recently
wrote on an application of multiple regression to gold trading. Virtually all
introductory
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">books on
statistics have a detailed discussion of the linear regression
method.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Successful
professional traders emphasize the importance of having a trading plan. A
trading game plan,
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">much like
that of a football team, clearly defines specific actions under different
conditions. The linear
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">regression
method is very useful in developing a forecast for the next trading day's high,
low and close
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">based on
the last five trading sessions. The method is general and broad-based enough so
that it can be
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">used with
stocks, indices or commodities. The forecast is the basis of my trading plan: I
can define what I
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">should do
if the market rises above the forecast high, falls below the forecast low or
stays within the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">forecast
range. This way, I can avoid being emotional and trade as mechanically as
possible by having a
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">plan to
rely on.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 9pt">FORECASTING WITH LINEAR
REGRESSION
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">I like to
use at least 10 days of data and develop a forecast for the high, low and close.
The five-day
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">regression
is a good choice for short-term trading. You can use any length of regression
you like. Here
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">are the
calculations with the daily close in a spreadsheet format:
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">1 Perform
a linear regression with the first five days of data to obtain the slope m
and constant c such
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>that
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">X
Value Daily Close
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
1 Day
1
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
2 Day
2
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">
....
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
5
Day 5
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">2 Forecast
the next day's close with the slope m and constant c from step
1:
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">(2)
Forecast close (Day 6) = 6m + c
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">3 Record
m, c and r 2 on the same line as Day 5. Record the forecast from step 2
one day ahead, with
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Day 6.
Note when we are using five days' data, the first forecast is for Day
6.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">4 Step the
calculation ahead one day such that
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">5 Record
m, c and r 2 as in step 3.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">6
Calculate the regression forecast oscillator, %F, as
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>(3)
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 10pt">%F = ((Y-Yforecast)/Y)*100
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">where Y is
the close for Day 6 and Y(Forecast) is the forecast for Day 6 from step 2 (from
Day 5).
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">7 Record
the oscillator on the same line as Day 6.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">8 Step the
calculations ahead one day at a time until the most recent day.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>Technically, we can use the linear regression to develop a point forecast
(single value) for the next day
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">(as in
step 2) or a range (interval) of values with a certain confidence level. The
interval widens, greater
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">the
variation in the data and greater the desired confidence level.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">I use the
forecast oscillator, %F, to determine if my forecast is above or below the
actual market data.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>Since
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 10pt">%F = ((Y-Yforecast)/Y)*100
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 10pt">
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 10pt">where Y can be any market variable
for stocks, indices or commodities, %F measures the percent
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">deviation
of the actual value from its forecast. In a trading market, %F changes its sign
before a
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>significant trend change. In trending markets, %F tends to change sign
early in the trend. I interpret %F in
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">the
context of the r 2 Of
the regression. A low value of r 2
plus a change in sign of %F is a good signal of a
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">change in
trend. Market extremes and periodicity can also be observed on the %F
charts.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 9pt">DEVELOPING A TRADING PLAN
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">You can
use the forecasts to develop a specific trading plan to suit your trading style.
I use the forecasts
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">in several
ways.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>Forecasts as stops. I use the high and the low as action
points. If the market exceeds the forecast high, it
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">wants to
go up. To trade with the trend, I put a buy stop a few ticks above the high. If
the market falls
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">below the
forecast low, it wants to go down. Hence, I set a sell stop a few ticks below
the forecast low. If
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">you want
to trade against the trend, sell short near the forecast high and buy near the
forecast low.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>Forecasts as intraday range scale. The forecasts provide a
scale for evaluating the trading day. The
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">market can
stay within the expected range or go outside. On a down day, the intraday high
is well below
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">the
forecast high and may be below the forecast close. On an up day, the market
stays well above the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">forecast
low and often above the forecast close.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>General rules for trading with forecasts. Here are some
general rules:
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">• Use the
forecasts only if r 2 is greater than 0.1. Higher the value of r 2 , the greater
the confidence in the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>forecasts.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">• A trend
change is imminent when r 2 falls below 0.1. Prepare to close longs.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">• A trend
is in place if r 2 is greater than 0.6. As a trend follower, you could wait for
this value to be
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">exceeded
before opening positions. This would keep you out of short-term
fluctuations.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">• An early
warning of a trend change is provided by a zero-crossing of %F, the forecast
oscillator.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Prepare to
tighten stops and look for changes in slope and coefficient of determination
for
<FONT
size=3>confirmation.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">•A change
in trend is confirmed by a change in slope of the regression. Open positions in
direction of
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">trend
change. To trade against the trend, look for peaks in slope and strength of the
linear trend.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">•The trend
will usually change in the direction of %F.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">•Always be
prepared for a market move against the forecast. Use stops!
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">A
SAMPLE TRADING
PLAN
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">I have
developed a forecast for the high, low and close for January 20, 1992, from the
previous five
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">trading
days, seen in Figure 1. The market was making new highs the previous week. Was a
downward
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">movement
imminent? Let's look at the data from Friday, January 17, 1992:
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">The market
was trending moderately (0.4<= r 2
<0.6), but the forecast oscillator %F was negative
for
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">high, low
and close, warning of a possible change in trend. The relatively small slope of
the regression
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">for the
high meant the market was meeting resistance. The slope of the regression for
the close had turned
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">down from
the high values during the recent strong uptrend. The forecast, however, called
for a strong
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">close near
the highs of the day, but that seemed doubtful, given the low slopes in a
moderating trend. The
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">plan was
to watch for a change in trend. If the market opened weak, a bearish strategy
was called for. For
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">example, I
would consider buying the Standard & Poor's 100 Index <SPAN
style="FONT-SIZE: 9pt">OEX January 390 puts, or
selling
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">short the
S&P 500 March futures contract.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: Arial">The high daily volume of
OEX
index
options traded makes the S&P
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: Arial">100 index an interesting application
of me regression forecast
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: Arial">approach.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">The market
opened at the Friday close and weakness was evident at the open, as the S&P
500 futures
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">opened
lower. It was clear in early trading that the trend would be down, as the market
traded well below
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">the
forecast high and close. Clearly, the forecast range provided a good scale,
since it reinforced the
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">concept
that the market was weaker than the trend of the prior five days. A bearish
stance would have
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">been
profitable.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 9pt">THE NATURE OF REGRESSION
FORECASTS
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">The high
daily volume of OEX <FONT
size=3>index options traded makes the S&P 100 index an interesting
application
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">of the
regression forecast approach. I have examined a time period from early October
1991 to
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>mid-January 1992. The OEX
close and its forecast are in Figure 2; the r <SPAN
style="FONT-SIZE: 10pt">2 values in Figure 3; %F in
Figure
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">4, and
Figure 5 has %F around the mid-November plunge.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Several
observations can be made from the OEX
analysis. First, the forecast lags the <SPAN
style="FONT-SIZE: 9pt">OEX in an uptrend
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">or in a
downtrend. Second, the close and the forecast cross over several days before a
trend change. This
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">crossover
can be seen as a zero crossing in the %F chart. Significant trend changes are
preceded by
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">trendless
periods with values of r 2 <FONT
size=3>near zero. Strong trends are accompanied by high values of r <SPAN
style="FONT-SIZE: 10pt">2 and
regression slope.
These observations support the general rules of interpretation noted above. As
Figure 5
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">shows, %F
provided a timely warning of an impending trend change just before the
OEX fell 15.68
points.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">I have
included data for wheat (cash) from 1989 to indicate the use of this approach
with commodities.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">The market
showed significant trends during this period with good periodicity, as shown in
Figures 6, 7
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">and 8. The
%F zero crossings were timely indicators of trend change. Features observed with
OEX charts
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">are also
seen here; note in particular how %F can be used to identify extremes in the
market from Figures
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">4 and
8.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Simple
linear regression yields forecasts of the high, low and close for stocks,
indices or commodities.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">these
forecasts can be used to develop a trading plan. You can trade with the trend,
against the trend,
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">intraday
or interday. The forecast oscillator, %F, provides early warning of trend
changes taken together
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">with the
regression slope and coefficient of determination. This approach works best in
trending markets
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">or trading
range markets; it is only moderately useful in volatile markets with choppy
price action. These
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">objective
forecasts will let you trade less emotionally and more mechanically. Profits
will look up when
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">you can
look ahead.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none">Tushar
Chande holds a doctorate in engineering from the University of Illinois and a
master's degree in
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><FONT
size=3>business administration from the University of
Pittsburgh.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: Arial">REFERENCES
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Lafferty, Patrick [ 1991 ]. "A
regression-based oscillator," <SPAN
style="FONT-SIZE: 11.5pt; FONT-FAMILY: Arial">Technical Analysis of <SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: Arial">STOCKS <SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">& <SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: Arial">COMMODITIE<SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">S,
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Volume 9:
September.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Merrill, Arthur [1991]. "Fitting a
trendline by least squares," <SPAN
style="FONT-SIZE: 11.5pt; FONT-FAMILY: Arial">Technical Analysis of <SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: Arial">STOCKS <SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">& <SPAN
style="FONT-SIZE: 8pt; FONT-FAMILY: Arial">COMMODITIE<SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">S,
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Volume 9:
December.
<P class=MsoNormal
style="MARGIN: 0in 0in 0pt; mso-layout-grid-align: none"><SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Pfaffenberger, Roger, and James
Patterson [1987]. <SPAN
style="FONT-SIZE: 11.5pt; FONT-FAMILY: Arial">Statistical Methods for Business
and Economic<SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">s,
<SPAN
style="FONT-SIZE: 11pt; FONT-FAMILY: Arial">Irwin.
<FONT face=Tahoma
size=2>-----Original Message-----From:
owner-metastock@xxxxxxxxxxxxx [mailto:owner-metastock@xxxxxxxxxxxxx]On
Behalf Of Steve KarnishSent: Thursday, January 10, 2002 10:34
AMTo: metastock@xxxxxxxxxxxxxSubject: Forecast
Oscillator
List,
Does anyone have the math formula for Chande's
Forecast Oscillator?
Thanks,
Steve
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