One of the most important features of * QuanTek*
is its

These **scrolling graphs** also have the property
that you can move to any part of the graph by **scrolling**
and **switching views**. (The **blue**
toolbar arrows **scale** the graph up or down, while
the **magenta** toolbar arrows **switch**
between different **views** along the horizontal axis.)
When you scroll the horizontal scroll bar, the vertical scroll bar
moves automatically to keep the center line of the graph centered in
the display. You can also adjust the vertical scroll bars yourself,
if necessary. So by **scrolling** and **switching
views**, you can move to any part of the **2048-day
graph**, which forms a single **graph view** of
the past **2048 days** of **corrected prices**.

**Note:** The scale on the right shows the **
prices** for stocks, so long as they lie in a reasonable
range. However, if the **price range** is too high or
too low, or it is an **index** or **mutual fund**,
then the price scale is replaced by a symbolic scale with the
**current price** indicated by dollar signs. The price
for all securites at any point is also indicated by **tooltips**.
If you move the mouse pointer anywhere in the graph, it displays the
**date** and **price** corresponding to
that point. So you can find the price at any point in the graph just
by moving the mouse pointer to that point, no matter what the range
of the price.

We begin with **Scale 4**, since this scale is
displayed initially when a graph opens. Here is a graph of **
Amazon**:

On this scale you see the **512-day (acausal)
Savitzky-Golay Smoothing Curve** (yellow curve in center).
The **"acausal**" means that at any point, the
smoothing mixes up both **past** and **future**
data -- the smoothing is over the whole graph at once. Hence as time
progresses, the smoothing curve at past points can change. But this
means that there is also **no time delay** in the
smoothing curve. This smoothing curve is also projected ahead
**N days**, where **N** is the **
Time Horizon** setting for the calculations (here, **32
days**). (The **present** time is denoted by
"ZERO".) So it provides yet another kind of **Price Projection**,
abeit a simple one.

Surrounding the **S-G Smooting Curve** are the
**Bollinger Bands**. These are spaced from the **
S-G Curve** by **1x** and **2x**
the **average absolute deviation** of the prices from
the **512-day S-G Smooting Curve**. This is the average **
trading range** to be expected normally, in the absence of
any **exogenous events**. These curves also serve as
**overbought/oversold indicators**. In the above graph,
you can see that the price in September appears **overbought**,
ranging above its outer **Bollinger Band**, and then at
the end of December it undergoes the **selling climax**
and becomes **oversold**, ranging below its outer
**Bollinger Band**. Presumably, due to the **
return to the mean** mechanism, the price will tend to return
back to the central **S-G Smooting Curve**.

In blue on the right is the **Price Projection**,
due to the **Default Adaptive Filter**. (You can also
calculate a second filter of your choice and toggle the display back
and forth between the two for comparison.) The calculates the
**expected N-day return** and displays it as a straight
line, starting from the **average price** of the latest
trading day (average of open, high, low, close prices). This **
expected return** is also displayed in the header
information. The **Default Aptive Filter** used is a
**Least-Mean Square** filter, which is a **
low-pass filter**. Hence any features shorter in duration
than **N days** (in this case, **32 days**)
does not have much effect on the **Price Projection**.
Generally, but not always, the **Price Projection** is
an indicator of the **long-term trend**. This can be
seen above since the **Price Projection** is
approximately parallel to the **projection** from the
**S-G Smooting Curve**. The fluctuations shorter than
**N days** are averaged out and only the **
long-term trend** remains. When presented as above, the
**Price Projection** is close to what the **
Random Walk** model would predict. (Except the **Random
Walk** model does not make clear how the **long-term
trend** is to be computed -- it takes the **long-term
trend** as fixed *a-priori*.)

The blue bars on the **Price Projection** are
**error bars**. Just as the **Price Projection**
represents the **expected N-day return**, the **
error bars** represent the **expected N-day range**
of prices. This is obtained by measuring the **average
absolute deviation** (**1-day range **or**
high** minus **low**) of the **log prices**, and
then multiplying this by the **square root of N**, for
**N future days**. (This is
only an **estimate**. There is also a direct
measurement of the **average N-day range**
available on the toolbar, which usually turns out to be smaller than
this **estimate**, so it is a *conservative*
estimate).

Also notice the green arrows which are **Buy Points**.
There are also red arrows above the graph which are **Sell
Points**. These correspond to the **Relative Price
(band-pass)** display which is a type of **oscillator**.
So these arrows represent **N-day inflection points**
in the **Relative Price** graph. But the **Buy
Points** are only shown when the **Price Projection**
is positive, and the **Sell Points** are only shown
when the **Price Projection** is negative. These
**Buy/Sell Points** are useful for **swing
trading**. They also depend on the setting of the **
Range** control in the **Trading & Portfolio Parameters**
dialog.

The graph along the bottom is the **logarithmic volume**,
relative to its average value. The bars range from the average (log)
value to a factor of 10 above and below the average value of the log
volume. (Since the logarithmic values are plotted, multiplying and
dividing the volume by 10 corresponds to the same distance above and
below the average log value.) The **volume** has been
extended to future values using the **Standard LP**
filter, mainly for aesthetic reasons. (The number in the lower right
corner is the size of the data set. However, only 2048 days are
used.)

Here is the graph of **Amazon** on **Scale 8**.
Both horizontal and vertical axes are doubled in size from **
Scale 4**, preserving the **aspect ratio**. In
other works, the **slope** of all graphs is preserved,
enabling direct comparison of **N-day returns** over
any interval:

Notice how all the slopes are preserved between the two graphs.
But all the features are twice as large. You can compare the **
risk** of different securities by comparing the width of the
**Bollinger Bands**, but you must do this with all
securities on the same **scale**.

The main feature that distinguishes this graph is that the daily
prices are represented by **candlesticks**. These
display the price range from **low** to **high**
by a vertical line. The **open** and **close**
prices are represented by the upper and lower edges of the
rectangles. If the **close** is higher than the **
open**, the rectangle is **light blue**, and if
the **close** is lower than the **open**,
the rectangle is **dark blue**. This provides a way to
display the **open** prices, which are not displayed in
the more usual method as in **Scale 4**.

In **Scale 4** the **Buy/Sell Points **
were displayed as **green/red arrows**. **Scale 8**
does not display these, but instead displays **Buy/Sell
Signals** as **green/red rectangles**. The
difference is that the **Buy/Sell Signals** are derived
from the **Relative Price
(low-pass)** display which is a type of **
overbought/oversold** indicator. It corresponds closely to
the **price level** relative to the **Bollinger
Bands** on the graph. There are no **green/red
rectangles** on this particular graph, but in other areas of
the graph they may be seen just **below/above** the
range of prices. This is because they indicate the optimum **
buy/sell levels** for **GTC buy/sell orders**.
The level at which these are set depends again on the **Range**
control in the **Trading & Portfolio Parameters**
dialog. Thus, despite appearances, the prices in the above graph, on
a **32-day average**, are actually within a normal
**trading range** and hence do not trigger the **
buy/sell signals**. On a shorter time scale, or with a
different setting of the **Range** control, the **
buy/sell signals** might be displayed at the price extremes
of the above graph. (They can also be displayed in the **
future Price Projection** by means of the **future
projection** of the **Relative Price**
indicator, via the **Standard LP** filter.)

Here is the graph of **Amazon** on **Scale 16**.
Both horizontal and vertical axes are doubled in size from **
Scale **8, preserving the **aspect ratio**. In
other works, the **slope** of all graphs is preserved,
enabling direct comparison of **N-day returns** over
any interval:

As in **Scale 8**, the daily
prices are represented by **candlesticks**. These
display the price range from **low** to **high**
by a vertical line. The **open** and **close**
prices are represented by the upper and lower edges of the
rectangles. If the **close** is higher than the **
open**, the rectangle is **light blue**, and if
the **close** is lower than the **open**,
the rectangle is **dark blue**. This provides a way to
display the **open** prices, which are not displayed in
the more usual method as in **Scale 4**.

This graph is very big and I thought it
would be a good place to plot the actual **historical Price
Projections**. In other words, the **Price Projection**
for all days in the past is plotted on this graph for each
corresponding day. For a given day
in the past, the **positive** price projections are
marked by a little green rectangle at the **close**
price, and the **negative** price projections are
marked by a little red rectangle at the **close**
price. Then, for the **N-day Price Projection, **the
projected price for each given day is shown by a
double-triangle, **green** for a **positive Price
Projection** and **red** for a **negative
Price Projection**. These **N-day Price Projections**
for each day are called the **N-day Price Target** for
that day.

This can also be viewed as a representation of the **Long/Short
Signals**, which are just the **estimated
returns** from the **Price Projections**. The
green/red rectangles mark the days for which the **Long/Short
Signals** are triggered. These
are also plotted as the **N-day Projected Future Returns**
in one of the **splitter windows**. Whether these
**Long/Short Signals** are triggered depends on the
setting of the **Threshold** control in the **Trading & Portfolio Parameters**
dialog. So the **Long/Short Signals** represent intervals in which the **optimal
position** should be **long/short**, according
to the **Price Projection**. Note that, once again, the
**expected return** of the **N-day Price
Projection** represents an **N-day smoothed optimal position**. The short-term price
fluctuations in the graph do not affect the **slope**
of the **Price Projection** very much, and hence the
**optimal position** is also not affected very much by
these short-term price swings.

Going down now in scale from **Scale 4**, we have a
graph of **Amazon** on **Scale 2**. Once
again, the **aspect ratio** is preserved:

Just as in **Scale 4**, the **Buy/Sell Points**
are displayed as **green/red arrows** on **Scale
2**. However, on this scale, instead of displaying a **
512-day Savitzky-Golay Smoothing Curve**, the **
2048-day (Robust) Trend Line** is displayed. The slope of
this line, denoting the **average 2048-day return**, is
displayed in the header instead of the slope of the **Price
Projection**. This is another, probably better, display of
**overbought/oversold** conditions. In fact, according
to this display, the recent **sell-off** and **
selling climax** shows up merely as a correction from a very
**overbought** condition back to the normal **
trend-line**. Then the **Bollinger Bands** are
drawn with respect to this **long-term trend-line**
instead of the **SG Smoothing Curve**.

Another feature of this graph is the **200-day Simple
Moving Average** (in gray). This is such a popular indicator
that we decided to include it. However, the **200-day MA**
is computed with respect to the **long-term trend-line**,
not some other way. This means that, going to longer and longer term
MAs, they will converge to the **long-term trend-line**.
Here might be a good place to also point out that you can plot a
wide variety of **exponentially weighted moving averages**,
in whatever color you want. These are also computed with respect to
the **long-term trend-line**. For completeness, you can
also plot **horizongal lines** at any price level, in
any color. (**Note:** If there are fewer than **
2048 days** of data, then that number of data days is plotted
on the graph, and the trend line is over that number of days.)

Finally, going down from **Scale 2**, we reach
**Scale 1**. This is a panoramic view of the price
action, with one pixel per data day. If your screen is 2048 pixels
wide, you can see the entire price action at once going back 8
years:

This scale has all the same features of **Scale 2**,
except that there are no **Buy/Sell Points** shown. But
the **200-day Simple MA** is shown on this scale. From
this bird's-eye view it appears that **Amazon** was
very **overbought** and the **sell-off**
and **selling climax** of the past few months merely
brought it back to its normal **trend-line**. This kind
of panoramic view is very useful to make such deductions, to avoid
the confusion and hysteria that occurs when everybody is just
looking at the short-term graphs (on a linear scale, without any
perspective).

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