** QuanTek** is a

** QuanTek** now works with either

For more information on all the features of ** QuanTek**,
please download the program and consult the

One of the best features of ** QuanTek** is
the

The **Main Graph** has four different scales, and
enough ranges on each scale to cover the whole 2048-day data set.
There are different **Trend Lines**, **Moving
Averages**, **Bollinger Bands, Buy-Sell Points**,
and **Candle Sticks** on the different scales. On each
scale is the **Price Projection** from the **
Wavelet Adaptive Filter**, showing the future **
expected return** on the time scale of your choosing.

The **Price Projection** is computed from a **
Wavelet Adaptive Filter** of our own design, which is a
**Least Mean Square (LMS)** type using regressors or**
Technical Indicators **obtained by means of **Wavelet
Smoothing**. The use of the **wavelet**
decomposition results in a dramatic simplification of the filter
design, and aids in separating the weak "signal" present in the data
from the "noise". Basically, the **wavelet**
decomposition separates the signal with respect to both frequency
and time, with the frequency separation in octaves and the time
separation longer on the low octaves and shorter on the high
octaves. This is a natural separation for many real-world signals,
as the only part of the signal that is actually relevant to the
present time is that which occured most recently, on the order of
the most recent few cycles on each octave. Then the **adaptive
filter** can utilize the most recent part of the signal on
each octave level for regression. At present we use the **
wavelet decomposition** of three different combinations of
the price data, which we call the **Relative Price**
(detrended prices), the **Velocity** (returns or 1st
difference of prices) and **Acceleration** (2nd
difference of prices). Actually, the **Acceleration**
indicator is very similar to the **Relative Price**, so
instead we also use the **Volatility** (absolute
deviation of prices). Use of the most recent values of the **
Relative Price**, **Velocity**, and **
Volatility** indicators as the regressors for the **
Wavelet Adaptive Filter** results in a vast simplification of
the filtering problem, as these three indicators are automatically
orthogonal (uncorrelated) on each wavelet level. In addition, using
the **Volatility** as one of the regressors makes the
filter an implementation of **GARCH (Generalized
Auto-Regressive Conditional Heteroskedasticity)**.

The **Price Projection** also displays **Error
Bars** which represent the **expected N-day
future price range** for

The **Price Projection** from the **Wavelet
Adaptive Filter** is optimized for a **Trading Time
Scale** from 1 to 128 days (10 days or greater recommended
using daily data), which you specify. This governs how rapidly the
**expected returns** change, and as a consequence how
rapidly the **Optimal Portfolio** changes. It also
governs the rapidity of the **Trading Rules**.

The **Optimal Portfolio** in ** QuanTek**
is computed using a modified

The **Portfolio Report** is an **RTF**
file that you can display at any time (after computing the **
Optimal Portfolio**). It shows the securities in the current
**Portfolio** folder along with the past returns on
several time scales, the future **expected return** on
the chosen trading **Time Scale**, and the **
standard deviation (volatility)**. Next it displays the
**model portfolio** which consists of the number of
shares long or short of each security "owned", the market value of
the shares, the actual price, and the basis price. Next some
portfolio information is displayed such as the account equity and
the total long and short market value. Finally the **optimal
portfolio** is displayed with the number of shares of each
security and percentage of equity, to compare with the corresponding
numbers in the **model portfolio**. It also displays
the **Sharpe Ratio** for each security, which is a
measure of the ratio of **expected return** to **
risk**. Finally the results of the **Optimal Portfolio**
calculation for the overall portfolio as a whole are displayed,
consisting of the **Expected Return** and **
Standard Deviation** for the whole portfolio, along with the
**Margin Leverage**. All this information is extremely
useful for making trading decisions. The **RTF** file
can be saved to disk and consulted later.

Most of this information can also be viewed in a dialog box
called the **Short-Term Trades** dialog. This dialog
also has a useful feature displaying the expected future price and
range of prices * N* days in the future,
where

* QuanTek* has several

Two other statistical tests are the **Wavelet Analysis**
and **Wavelet Variance** dialogs. These are mainly used
to test whether the **Wavelet** routines are
functioning correctly, and to display their output graphically. The**
Wavelet Analysis** dialog** **displays the
output of the **Wavelet** filters in terms of the
**wavelet coefficients** and the **
multi-resolution analysis (MRA)**. The **Wavelet
Variance** dialog uses the actual price data to compute its
**wavelet variance** and then display a **
covariance matrix** based upon it.

Next there are two statistical tests that show a standard
spectral decomposition of the price returns. The **Periodogram
Spectrum** displays a standard **Fourier**
spectrum of the returns. This is a standard computation in **
time-series analysis**. The **Wavelet Spectrum**
displays the corresponding **Wavelet** spectrum of the
returns, averaged over time, so there is one average value per
frequency octave. Theoretically, if the returns data are correlated
(assumed stationary, so the correlation is time-independent), then
the correlation would show up in a non-constant spectrum of the
returns. On the other hand, if the spectrum is constant, then the
returns are "white noise", in accordance with the **Random
Walk** model. Actually, though, the theoretical variance of
the spectrum is about 100%, so it is hard to tell from the spectral
graph alone whether there are really any meaningful correlations in
the data. (Also, the correlation is not expected to be stationary.)
This is why the **Correlation** test described above is
more relevant for non-stationary correlations.

Finally, there is the **Correlation -- Returns**
dialog. This dialog measures the **correlation**
directly between two securities, or the same security, in which you
can vary the time lag between the two. The result is displayed in
the form of a **scatter graph**, with a point on the
graph for each point of the data. If there is **correlation**,
it can be seen as a non-uniform distribution of the points on the
graph. The actual degree of **correlation** is
displayed, computed three different ways, along with the confidence
level that the correlation is not spurious. There is also another
dialog connected with this one, that displays the **
auto-correlation **or** cross-correlation**
**sequence** between the same two securities, as a
function of time lag. This **correlation** uses the
**Fourier** **transform** method. The
**Correlation -- Returns** dialog could be useful for
choosing securities in the **portfolio** to achieve
maximum **diversification**, since to achieve this it
is important to find pairs of securities that are **
anti-correlated**.