In addition to the **Main Graph**, the current
version of * QuanTek* comes with a set of
three

The first two **Indicator** windows each show three
different indicators, which are called **Relative Price**,
**Velocity**, and **Volatility**. The
**Relative Price** indicator is constructed from prices
with **wavelet smoothing** on two different time
scales. The shorter time scale is the **Time Horizon (N)**
which is set in the **Trading & Portfolio Parameters**
dialog. In fact, this setting determines the **smoothing time
scale** for all displays and filters in the program. The
longer time scale corresponds to the highest **wavelet levels**
and is of the order of **1028 days**. All the displays
are **causal**, meaning that at any point it time, they
are constructed only from **past data** relative to
that point. Each data point of the indicator is a separate smoothing
over the **past data** relative to that point. So the
**Relative Price** indicator consists of the difference
of the **causal wavelet smoothing** of the price on the
short and long time scales. In this way, the **Relative Price**
indicator is analogous to the usual **Moving Average
Convergence-Divergence (MACD)** indicator of ordinary **
Technical Analysis**. The other two indicators are the
**Velocity**, which is just the **N-day smoothed
returns**, and the **Volatility**, which is just
the **N-day smoothed average absolute deviation** of
**returns**. These three smoothed indicators are also
the **regressors** used in the **Adaptive Filter**
calculation.

The indicators are also smoothed usiing two different methods,
**low-pass** and **band-pass**,
illustrated below. The **low-pass smoothing** means
that the **wavelet levels** shorter than a certain
**time scale** are cut off and only the levels for
longer **time scales** are kept. The **band-pass
smoothing** means that only **wavelet levels**
in a small range corresponding to a certain **time scale**
are kept and both longer and shorter **time scales**
are cut off. Hence the **low-pass smoothing** contains
the very low-frequency signals, while the **band-pass
smoothing** does not.

In the displays below, the yellow vertical line denotes the
**present time**. The time scale at the bottom denotes
days in the past (negative) and future (positive). The indicator for
future days is obtained from the past indicator by means of **
linear prediction** using the **Standard LP Filter**.
The green/red vertical lines mark the positions of the **
Buy/Sell Points**, which are inflection points of the **
Relative Price (band-pass)** indicator (see the **
Indicators (band-pass)** graph). The horizongal orange lines
are the settings of the **Range** and **Threshold**
which are set in the **Trading & Portfolio Parameters**
dialog. These determine the levels at which the **Buy/Sell
Signals** and **Buy/Sell Points (Range)**, and
**Long/Short Signals (Threshold)** are triggered.

The **Indicators (low-pass smoothing)** window is
shown here for **Standard & Poors 500 (.SPX)**:

The **Relative Price** indicator with **
low-pass smoothing** is shown in the bottom pane. The **
low-pass smoothing** retains the **low-frequency**
components of the indicators. Thus this **Relative Price**
indicator can be interpreted as an **oversold/overbought
ndicator**, which I call the **Buy/Sell Signals**.
These indicate optimal **Buy/Sell** price levels due to
the **oversold/overbought** condition of the market.
For example, the **S & P 500** did not show much
activity up to a few weeks ago on the **Relative Price**
indicator, indicating that it was staying close to its **
long-term trend** and was not in an **
oversold/overbought** condition. But then about a month ago
it underwent a **sell-off** and **selling climax**,
and as a result the **oversold** condition is indicated
by the green region, giving rise to **Buy Signals**.
The regions where these signals are triggered can be adjusted by
varying the **Range** control. Also the **
Adaptive Filter Output** must be **positive/negative**
for the **Buy/Sell Signals** to be triggered. These
**Buy/Sell Signals** are shown as green/red rectangles
on the graphs on **Scale 8**.

The **Velocity** indicator is just the smoothed
**returns**, in this case with **low-pass
smoothing**. The **returns** do not have many
**low-frequency** components, so there is not too much
difference between the **low-pass** and **
band-pass** display for the **Velocity.** The
**Volatility** display is the **average absolute
value** of **returns**, so this display is
always positive. It is still positive using **low-pass
smoothing**, so in this display it is shown relative to the
zero point at the bottom of the graph. No **indicators**
are derived from the **Velocity** or **Volatility**.

The **Relative Price** may be thought of as
corresponding to the **return to the mean**
correlation. The **Velocity** may be thought of as
corresponding to the **trend persistence** correlation,
and the **Volatility** corresponds to **GARCH.**
In the **Adaptive Filter** calculation, all **
wavelet levels** of these indicators are used as **
regressors**.

The **Indicators (band-pass smoothing)** window is
shown here for **Standard & Poors 500 (.SPX)**:

The **Relative Price** indicator with **
band-pass smoothing** is shown in the bottom pane. The
**band-pass smoothing** cuts off the **
low-frequency** components of the indicators. Thus this
**Relative Price** indicator can be interpreted as an
**oscillator** type of** indicator**,
which I call the **Buy/Sell Points**. These indicate
possible **Buy/Sell** points for **short-term
trading** or **swing trading**. In this example,
the **S & P 500** is showing** short-term
fluctuations** even though it is remaining close to its**
long-term trend**. The** Buy/Sell Points** are
triggered when there is an** N-day inflection point**
in the **Relative Price**.** **The regions
where these points are triggered can be adjusted by varying the
**Range** control. Also the **Adaptive Filter
Output** must be **positive/negative** for the
**Buy/Sell Points** to be triggered. These **
Buy/Sell Points** are shown as green/red arrows on the graphs
on **Scales 4** and **2**, and as
green/red vertical lines on all the **Indicator**
windows.

The **Velocity** indicator is just the smoothed
**returns**, in this case with **band-pass
smoothing**. The **returns** do not have many
**low-frequency** components, so there is not too much
difference between the **low-pass** and **
band-pass** display for the **Velocity.** The
**Volatility** display is the **average absolute
value** of **returns**, so this indicator is
always positive. The display is positive or negative using **
band-pass smoothing**, however, so in this display it is
shown relative to the zero point at the center of the graph. No
**indicators** are derived from the **Velocity**
or **Volatility**.

The **Relative Price** may be thought of as
corresponding to the **return to the mean**
correlation. The **Velocity** may be thought of as
corresponding to the **trend persistence** correlation,
and the **Volatility** corresponds to **GARCH.**
In the **Adaptive Filter** calculation, all **
wavelet levels** of these indicators are used as **
regressors**.

The **Adaptive Filter Output** window is shown here
for **Standard & Poors 500 (.SPX)**:

The bottom pane shows the actual output of the **Adaptive
Filter**, which is the **N-day projected return**
at each day in the past. (In this case, **N=32 days**.)
This means that the filter was calculated with a **Time
Horizon** setting of **N=32 days**, which has
been set in the **Trading & Portfolio Parameters**
dialog. The filter parameters have been set so that the filter gives
the nice, smooth output shown above. This means that the filter is
responding mainly to the **long-term trend** and not to
**short-term anomalies**, such as the recent **
sell-off** and **selling climax**. Nevertheless,
it can be seen that the **projected return** has
decreased a little bit over the past month, due to this. The output
of the **Adaptive Filter** is an indicator that I have
named the **Long/Short Indicator**. This is because if
the **projected return** is **positive/negative**,
the recommended position is **long/short**. The **
Long/Short Signals** are triggered by the **projected
return** being outside the **Threshold,** which
has been set in the **Trading & Portfolio Parameters**
dialog. If this is the case, it is shown in green/red; otherwise if
it is inside the horizontal orange lines, it is shown in blue.

The **Actual 'Future' Returns** pane in the middle
shows just that -- at each point in the past the **actual
N-day 'future' returns** relative to that point in the past.
(Of course, these 'future' returns are made up of past data.) These
are the actual **N-day returns** that the **
Adaptive Filter** is trained on as it steps one day at a time
into the future and the **filter coefficients** are
adjusted to fit this data. In the filter computation, these **
N-day 'future' returns** are extended by the **N-day**
linear trend when within **N** days of the present.
Then this display is extended by **Linear Prediction**
into future days, as are all the **indicators**. So
this is the graph that the **Adaptive Filter output**
should reproduce if the data were** perfectly correlated**,
which of course it is not.

The top pane shows the** 2048-day Long-Term Trend**,
or in other words, the slope of the **2048-day (robust)
trend-line, **extended into the future to make an **
alternative Price Projection**. As can be seen, the slope of
this **long-term trend-line** is not constant, although
it changes slowly. The **Adaptive Filter output**
actually reproduces this **long-term trend-line**
more closely than the **N-day 'future' returns** that
it is trying to emulate. This is because the **Adaptive Filter**
is a **low-pass filter** and it responds mainly to the
**low-frequency** components of the signal, which are
the ones that contain most of the **correlation**. This
is a good thing, because it eliminates **excessively erratic**
trading and hence greatly reduces the **risk**. Most of
the **reward** comes from taking advantage of the
**overbought/oversold **conditions, which are slowly
changing in general. This **2048-day Long-Term Trend**
is what is used to estimate **N-day expected return**
in the **Optimal Portfolio**, and the **risk**
is just the **2048-day average volatility**. So (in
this version of ** QuanTek**) the

*Go back to ***QuanTek Features**