(Posted December 1, 2001)

** StockEval** has a
number of technical indicators, but they are of a different sort than the
traditional ones. Several of these are combined on the Main Graph to give a
clear picture of the technical situation of the stock at any given time. There
is also a set of six indicators in two splitter windows that are of the
traditional form of a graph, but these indicators are different than the traditional
ones. As explained below, each of these actually combines several of the
traditional indicators. The technical indicators in

** StockEval** has two
sets of three indicators, in two splitter windows, which have been named the

The bottom pane of
the *Harmonic* *Oscillator*, which is the *Relative Price*,
shows the price fluctuations relative to the *Reference Curve*. The
digital smoothing essentially picks out the N-day and longer price fluctuations
from all the shorter period Fourier modes. For N-day trading, you buy at a
(local) minimum of this curve and sell at a (local) maximum. This indicator
may be thought of as the smoothed version of the price fluctuations within the *Bollinger
Bands* on the Main Graph. When the daily price moves outside the *Bollinger
Bands*, the *Relative Price* indicator will be colored red or green,
showing that the **sell stop** or the **buy stop**, respectively, are in
effect.

The middle pane of
the *Harmonic* *Oscillator*, which is the *Velocity*, is the
first derivative, or rate of change, of the *Relative Price*. This is the
indicator that is most similar to the majority of the normally used technical
indicators, as will be described below. It indicates the *slope* of the
tangent line to the bottom curve. When this slope is zero, there is a minimum
or maximum of the bottom curve, corresponding to a buy or sell signal. So when
the Velocity goes through zero from negative to positive, this indicates a buy
signal, and when it goes through zero from positive to negative, this indicates
a sell signal.

The upper pane of
the *Harmonic* *Oscillator*, which is the *Acceleration*, is the
second derivative, or curvature, of the *Relative Price*. This indicator
should reach a positive maximum at a buy point (positive curvature) and a
negative maximum at a sell point (negative curvature). In a classical harmonic
oscillator from physics, the oscillator itself would be represented by a sine
wave, the velocity of the oscillator would be the same sine wave except 90
degrees ahead in phase, and the acceleration of the oscillator would be the
same sine wave except 180 degrees ahead in phase. This is indeed approximately
true in the case of the *Harmonic Oscillator* indicator (at least, for the
N-day fluctuations).

The bottom pane of
the *Technical Indicators* displays the recommended N-day position, or *Trading
Rules*, with the centerline corresponding to the normal or Core position.
This indicator is a combination of appropriate functions of the three
components of the *Harmonic Oscillator* indicator, as described above.
You set the combination of the three components by means of three slider bars
in the *Trading and Portfolio Parameters* dialog box. The buy/sell points
indicated on the Main Graph as green and red rectangles, and on both splitter
windows as green and red lines, are derived from the *Trading Rules*
indicator. On the Main Graph, the first buy and sell points have a green and
red horizontal line extending back to the present point in time, to indicate
the recommended buy/sell levels for GTC limit orders. When the daily price
moves outside the *Bollinger Bands*, the *Trading Rules* indicator
will be colored red or green, showing that the **sell stop** or the **buy
stop**, respectively, are in effect.

The middle pane of
the *Technical Indicators* displays the *Price Momentum* indicator,
which is the difference between the daily (logarithmic) close and open prices
multiplied by the actual volume, then subjected to N-day smoothing. This is
intended to display the rate of change of accumulation/distribution. When the *Price
Momentum* is positive, this is a buy signal, and when it is negative, this
is a sell signal.

The *Volatility*
indicator displays the spread between the (logarithmic) high and low daily
prices, subjected to N-day smoothing. This indicator should be of use to
short-term traders in estimating the relative degree of N-day price movements.

With one of the stock data files open, choosing *Harmonic Oscillator*
will display the *Harmonic Oscillator* splitter window:

In this splitter window, you can see the three technical indicators that
make up the *Harmonic Oscillator* indicator. The bottom indicator,
called the *Relative Price*, is the N-day smoothed price relative to the
256-day smoothed *Reference Curve*. It is similar to a type of **MACD**
indicator, except that there is no time lag. This is the indicator you
would use in a *Buy Low--Sell High* type of strategy. Above it is
the *Velocity* indicator, which is the rate of change of the *Relative
Price*. It shows the slope, or rate of change, of the N-day smoothed
price (relative to the *Reference Curve*). This is the indicator you
would use in *momentum* trading. The top indicator is the *Acceleration*,
which shows the curvature of the *Relative Price*. This indicator
shows the turning points of the *Relative Price*; positive curvature for a
buy point and negative curvature for a sell point.

Through all three graphs you will note green and red vertical lines.
These correspond to the *buy/sell points* displayed on the *Main Graph*.
They are derived from the *Trading Rules* indicator on the *Technical
Indicators *splitter window. In turn, this latter indicator is
constructed from the three indicators of the *Harmonic Oscillator*.
You will note that the green buy points pass very nearly through the minima of
the *Relative Price* curve, and the red sell points pass very nearly
through the maxima of the *Relative Price *curve. In turn, the green
buy points pass very nearly through the zero points moving upward, and the sell
points through the zero points passing downward, of the *Velocity*
indicator. Similarly, the green buy points pass very nearly through the
maxima, and the sell points through the minima, of the *Acceleration*
indicator. This corresponds to the *Velocity* being the first
derivative, and the *Acceleration* being the second derivative, of the *Relative
Price*.

Note that the *present time* is indicated by the vertical yellow line
which passes through the ZERO point on the time scale. The rest of the
time scale is in days relative to the present. The future buy/sell points
tend to move around as the historical data are updated every night, but you can
time your trades by estimating the point at which the green and red lines pass
through the yellow line, denoting the present. This will give you good *approximate*
buy/sell points.

The part of the *Relative Price* indicator colored in red indicates
that a **sell stop** is in effect, because the (average) price lies below
the outer *Bollinger Band*. This means that all long positions
should be liquidated, and you will notice that there is no buy point
recommended at that point. If the price is above the upper *Bollinger
Band*, where a **buy stop** is in effect, then the *Relative Price*
indicator will be colored green. This means that all short positions
should be liquidated, and there will be no sell point recommended at that
point.

With one of the stock data files open, choosing *Technical Indicators*
will display the *Technical Indicators* splitter window:

The bottom pane of the splitter window shows the *Trading Position *(or
*Trading Rules*) indicator, which shows the recommended N-day short-term
trading position as calculated by ** StockEval**. (This does not
include the

The middle pane shows a *Price Momentum* indicator, which represents
the rate of accumulation/distribution. It consists of the daily close
minus open (logarithmic) price, multiplied by the actual volume. Thus, it
is a measure of the actual *significance* of a (daily) price move, since
it takes into account the volume of the move. This indicator may be
thought of as the rate of change of the *On Balance Volume* indicator.

The top pane shows the daily *Volatility* (after N-day
smoothing). This is the high minus low (logarithmic) price for the
day. It is known that the two-point correlations for non-linear functions
such as volatility are not random; hence the **Linear Prediction** of this
indicator should be of special significance. The *Volatility*
indicator may be of use in timing your trades on an intra-day basis.

If you choose *Show Short-Term Trades* from the toolbar, or right-click
the mouse anywhere in the program, this brings up the *Short-Term Trading*
dialog box:

This dialog box is useful because it encapsulates all the trading and
recommended position information in one place. It contains a list of all
stocks in the *Stock Group* which are included in the portfolio by having
their *Trade this stock?* check box checked (in the *Form View*).
For each stock the current position, Core Position, N-day Position, and
recommended GTC buy/sell positions and prices are shown. By clicking on any
stock on the left, the right-hand list box shows the expected *average price*
and *volatility range* for the upcoming trading day, calculated by **Linear
Prediction**. (The volatility limits correspond to the Prices where the
Position is indicated as 100%. The Position indicates the percentage of
the volatility range.) Below that are the Last Average, Open, High, Low,
and Price, which you can get intra-day by doing an *Intra-day Update* from
**Dial/Data**. If the last update was end of day, these are the end of
day prices. The date and time of the last intra-day or end of day update
is recorded in the upper right corner of the dialog box. So this *Short-Term
Trading* dialog box is very useful for organizing your trading activities
during market hours.

The *Harmonic Oscillator*
indicator is now considered again, and each component compared to the usual
technical indicator to which it is most similar.

**Moving Averages:**
The N-day smoothing of the price graph is, of course, similar to a (simple)
moving average. The main difference is that the smoothing uses both *past*
and *future* data, and has no time delay, unlike the moving average, which
uses only past data. Close to the present day, the smoothed data must make use
of the future projected prices a projection routine. Also, the *Savitzky-Golay*
digital smoothing filter preserves the shape of features with a period longer
than N days, better than the moving average. The difference of two smoothings
with different time periods may be used in a similar fashion to the difference
of two moving averages, except for the fact that there is no time delay in the
smoothing. So if the price is trending uniformly upward or downward, the two
smoothed price curves will not lead or lag one another (unlike the two moving
averages). In the case of two moving averages, this time delay means that the
difference of the two moving averages functions similarly to a *derivative*
of the price curve. The difference of two smoothings may be used to indicate a
short-term fluctuation relative to a longer-term average, but since there is no
time delay the difference does not function as a *derivative*. On the
other hand, derivatives may be calculated from the *Savitzky-Golay* digital
smoothing filter directly.

**Moving Average
Convergence Divergence (MACD):** The standard MACD indicator is the
difference of two exponentially weighted moving averages, the slower moving
average of 130 trading days, and the faster one of 60 days. The
difference is then smoothed by a 45 day moving average. This is somewhat
similar to what is done in the *Relative Price* indicator, except that the
*Savitzky-Golay* digital smoothing filter is used instead of exponentially
weighted moving averages, thereby eliminating the time lag. In the *Relative
Price* indicator, with the trading time scale set to N days, the difference
is taken between the N-day smoothed price and the *Reference Curve*
consisting of the 256-day smoothed price. The result of this is that the
short-term modes with periods less than N days are eliminated by the N-day
smoothing, and the long-term modes with periods greater than 256 days are
eliminated by subtracting the *Reference Curve*. This produces a
type of oscillator, with no time lag, in which the predominant modes have
periods close to N days.

**Williams'
Percentage Range (Percentage R):** This indicator takes the prices over the
past N-day time interval, then plots the current price as a percentage of the
price interval between the highest and lowest price within that time interval.
It thus displays the current price within the trading range established over
the past N days. If this indicator were smoothed out by eliminating the
shortest-term fluctuations, then it would be essentially the same as the N-day
fluctuations in the *Relative **Price* part of the *Harmonic
Oscillator* indicator. Both indicators show when the price swings have
reached *oversold* and *overbought* limits, indicating buy/sell
points respectively. The main difference is that the *Relative **Price*
indicator filters out the daily price fluctuations, leaving only the N-day (and
longer) fluctuations, and it shows the overbought/oversold conditions relative
to the long-term trend, not relative to the N-day range of prices. This is in
accord with the overall trading strategy of ** StockEval**, which is
that overbought/oversold conditions relative to the short-term average do not
have much relevance. The

**Oscillator:**
The traditional Oscillator of Technical Analysis is closely related to the *Velocity*
part of the *Harmonic Oscillator* indicator of ** StockEval**.
The traditional Oscillator is just the difference between the most recent
closing price and the closing price N days ago, expressed as a point within the
range of prices covered within the last N days. This range of prices is
usually normalized to the interval between -1 and +1. But the traditional Oscillator
can be seen to be the average price velocity over the past N days. However,
once again, it can be seen that the traditional Oscillator contains far less price
information than the

**Wilder's
Relative Strength Index (RSI):** This index is also similar to the *Velocity*
of the *Harmonic* *Oscillator* indicator in that both are related to
the first derivative of the N-day smoothed prices. The *Velocity*
indicator shows this directly, of course. The RSI indicator is a more indirect
measure of the first derivative and is again lagged in time by N/2 days. The RSI
indicator is constructed by counting the number of Ups and Downs over the N day
interval. An Up is the difference in closing price on a certain day minus the
closing price the day before, if this quantity is positive, and zero if it is
negative. Likewise, a Down is the difference in closing prices if it is
negative, expressed as the absolute value (a positive number), and zero if the
difference is positive. The RSI is then defined as the sum of all the Ups
divided by the total Ups plus Downs over the N-day interval, multiplied by
100. It thus ranges between zero and 100. (They should have defined it as
(Ups - Downs)/(Ups + Downs), a number between -1 and +1, but oh well.) This
indicator still contains less price information than the *Velocity* of the
*Harmonic* *Oscillator* indicator, since it still uses only closing
prices. The RSI indicator actually contains essentially the same information
as the traditional Oscillator described above, since the modified version of
the RSI that was just suggested is virtually identical to the definition of the
traditional Oscillator. (The (Ups - Downs) is just the difference in closing
prices between now and N days ago, and the (Ups + Downs) is roughly the
expected range in prices over the N days.) As before, the *Velocity *of
the *Harmonic Oscillator* indicator measures the same thing, except with
better "statistics" and no time lag.

** **

**Lane's
Stochastics:** This is a composite indicator consisting of the RSI indicator
over a short time interval, together with three moving averages of this
indicator. Actually, in Eng's book the definition of this indicator is a
little ambiguous, because although it is defined to use the RSI indicator, in
the actual description of how to set up the indicator it sounds more like it
uses a variation of the Percentage R indicator. However, there should not be a
whole lot of difference between a short time period RSI indicator and the
Percentage R indicator, so either will probably work. In both cases, the
overbought signals are at the troughs of the indicator, and the oversold
signals are at the peaks. To complete the Lane's Stochastics indicator, one
takes a short time moving average of the RSI or Percent R, then a moving
average of that moving average, and finally another moving average of the
second one. One plots the first two indicators together, and the last two
indicators together, forming two separate graphs. The buy/sell points are
indicated at the *crossover points* of the two moving averages in each
graph. Note now that comparing two moving averages with different time scales
is similar to the concept of taking a derivative, and the crossover points of
the MAs correspond to the zero-crossing points of the derivative. If RSI is
used, then this is effectively a way to determine a time-delayed second
derivative of the prices, while if Percent R is used; the result is effectively
a first derivative of the prices that is not time-delayed. In either case, the
crossover point is equivalent to the zero-crossing point of the *Velocity*
of the *Harmonic* *Oscillator* indicator. So, instead of comparing
two moving averages to effectively get the zero-crossing points of the first
derivative of the price graph, it is much better to calculate this quantity
directly by using the *Savitzky-Golay* smoothing filter in the *Harmonic
Oscillator* indicator.

**Lane's
Stochastics:** None of the usual indicators seem to calculate a second
derivative directly, although Lane's Stochastics calculates a kind of effective
time-delayed second derivative if one mentally pictures the difference of two
moving averages of the RSI indicator. However, it is much more straightforward
to calculate this smoothed second derivative directly using the *Savitzky-Golay*
smoothing filter in the *Harmonic Oscillator* indicator. This second
derivative, or *Acceleration* indicator should be used as a confirming
indicator to the *Relative **Price* and *Velocity* parts of the *Harmonic
Oscillator* indicator.

**On-Balance
Volume:** The *Price Momentum* indicator is the difference between the
daily (logarithmic) close and open prices multiplied by the actual volume, then
subjected to N-day smoothing. This is intended to display the rate of
accumulation/distribution, and may be thought of as the rate of change of the *On-Balance
Volume* indicator. (The *On-Balance Volume* is an integrated form of
the *Price Momentum* indicator.)

To be honest, it appears that
many of the standard technical indicators were devised before the days of
personal computers, and were constructed the way they were because they were
the only quantities that were easy to calculate by hand. The *Harmonic
Oscillator* indicator and other technical indicators in ** StockEval**
evidently contain the same information and are easier to interpret than these
standard technical indicators.

*return to ***
Demonstrations*** page*