# Omicron Research Institute

## Technical Articles

Here are a set of new new QuanTek articles that apply to the current version, a set of articles describing a Wavelet Linear Prediction filter, a set of old articles that apply to QuanTek 3.5, and finally a couple of short magazine articles. The new articles are the first five articles in the QuanTek Help file, in PDF format. They can be viewed in the Help file that comes with QuanTek, using the HTML Help file viewer, but these files in PDF format are much easier to read (because of the math equations). These articles open in a separate tab in your web browser, so to return to this page just click its tab.

### QuanTek Articles (new)

Overview and Main Features of QuanTek (PDF)  (Revised October 25, 2017)  This article gives a detailed overview of the entire QuanTek program. First is a discussion of the many Help dialogs and the main Help file, then how best to utilize QuanTek for short-term trading. Next comes a general discussion of Stochastic Processes and Filtering, which are the basis of how QuanTek works. Next is a detailed discussion of the features of the four main Graph scales in QuanTek, followed by a description of the Portfolio Optimization routines. Finally the Trading and Portfolio Settings are described.

Statistical Displays and Tests in QuanTek (PDF)  (Revised October 19, 2017)  This article begins by discussing some of the various possible mechanisms for inefficiency in the financial markets as a source of correlation in the financial returns.  We then discuss our generalized definition of a Technical Indicator, then discribe the Harmonic Oscillator indicators utilized in QuanTek. Then the basic design of the Linear Prediction filters used in QuanTek is described.  The article then goes on to describe the various statistical tests and displays in QuanTek, used to test for correlation between the Technical indicators and future returns, as well as to test and display the general statistical properties of market data.

Econometric Analysis in QuanTek (PDF)  (Revised October 7, 2017)  This article describes some of the theoretical background for the QuanTek program, with regard to the sciences of Econometrics and Signal Processing.  It discusses the concepts of Signal Pricessing, Linear Prediction, Wavelet Analysis, and Optimal Trading Strategies. It then goes on to discuss the Efficient Market Hypothesis and possibility of market inefficiencies. Then there is a discussion of Financial Returns as a Stochastic Process. Finally there is a discussion of Portfolio Optimization and Rebalancing.

Portfolio Optimization in QuanTek (PDF) ( Revised July 22, 2017)  This article describes the mathematical theory behind the method of Portfolio Optimization used in QuanTek. First the need for Portfolio Optimization is discussed. Then two different theories of Portfolio Optimization are discussed,  which are the standard Markowitz Mean-Variance Optimization (including the CAPM), and another version which we call Unconstrained Quadratic Optimization. These two methods are derived and compared in detail, and a practical problem with the Markowitz method is explained. Then the specific version of Unconstrained Quadratic Optimization used in QuanTek is described.

Bibliography (Quantitative Finance) (PDF)  (Revised September 20, 2014) This is a bibliography that I have compiled of all the books on Stock Trading and Quantitative Finance, and related topics, that I could find. This includes both references that I own and used to build the QuanTek program, as well as others that have been published that I do not own (marked with an asterisk.)

### Wavelet LP Filter Articles

Stationary Stochastic Processes (PDF)  (Revised October 25, 2012) This article is a basic review of the properties of Stationary Stochastic Processes. It describes the general design of Linear Prediction filters for such processes. The theory is developed in the Fourier basis, which is well-adapted to such processes. The theory of such LP filters for Stationary Stochastic Processes is much more highly developed than that for Non-stationary Processes, because the theory of such processes is much more highly developed.

Non-stationary Stochastic Processes (PDF)  (Revised April 10, 2012) This article develops a theory of Non-stationary Stochastic Processes. It describes the general design of a Wavelet Linear Prediction filter designed for such processes. The theory is developed in the Wavelet basis, which is better adapted to non-stationary statistics than is the Fourier basis. The theory of the LP filter in a non-stationary environment is developed, and the problem of inverting the covariance matrix is examined in detail. This problem becomes much easier in the Wavelet basis, since in that basis the covariance matrix may be taken to be approximately diagonal, the diagonal elements consisting of the Wavelet variance.

Wavelet LP Filter Design (PDF)  (Revised November 5, 2012) This article explains the details of a class of Wavelet Linear Prediction filters, which rely on the idea that the covariance matrix is approximately diagonal in the Wavelet basis. The diagonal components of the covariance matrix in this basis are the components of the Wavelet variance. The fact that the covariance matrix is diagonal enables a vast simplification of the filter design. Unfortunately, this filter design was not successful for financial data, because of the fact that the Wavelet variance itself consists largely of stochastic noise. However, this filter design might be very useful in situations in which the Signal to Noise ratio (S/N) is fairly high.

### QuanTek Articles (old)

Introduction to QuanTek (PDF) (Revised August 1, 2005) This article gives a general introduction to QuanTek 3.5, including a discussion of the Linear Prediction filter, the various statistical tests, the graphs, splitter windows, and other displays, and also the Day Trades dialog.

How to Use the QuanTek Trading Rules (PDF) (Revised May 19, 2005) This article is not contained in the QuanTek Help file, but it contains useful information nonetheless. It describes the features of the Main Graph, the construction of the Trading Rules utilizing the Momentum Indicators, and the three splitter windows displaying the Technical Indicators consisting of the Momentum Indicators, Harmonic Oscillator, and Trading Rules. This system is no longer used, as it has been replaced by an Adaptive Filter, which does the same thing only better.

Correlations and Technical Indicators in QuanTek (PDF) (Revised May 19, 2005) This article discusses the Technical Indicators used in QuanTek and the measurement of correlation between these indicators and future returns. It also discusses the effect of smoothing on the correlation. The statistical tests used to measure this correlation is described, and the Trading Rules derived from the Technical Indicators is also discussed.

Mathematics of the Random Walk Model (PDF)  (Revised April 12, 2004)  This article discusses the Random Walk Model and possible sources of inefficiency that could account for deviations from this model in real stock data.  Then a quantitative investigation of expected return and risk is made within the context of the Random Walk Model.  This investigation shows that even in the simplest possible scenario -- the Random Walk Model itself -- the mathematics can get extremely complex!

### Magazine Articles

Making a Price Projection Using Linear Prediction Filters  (Revised September 28, 2006)  This is a short article discussing the QuanTek Linear Prediction filter and some other features of QuanTek.

Using the Savitzky-Golay Smoothing Filter  (Revised October 19, 2006)  This article explains how the Savitzky-Golay digital smoothing filter can be used to good advantage in Technical Analysis to construct new, more sophisticated technical indicators.