WavSD for TradingSolutions
The WavSD (Wavelet Spectral Decomposition) for TradingSolutions is an addon product which allows TradingSolutions to perform the calculation of a Wavelet Sampling Filter (Native Wav) and a
Spectral Decomposition (SD) algorithm. WavSD is a modelfree tool for time series structure recognition and identification which decomposes the time series data into several additive components that can
be interpreted as smooth and slowlyvarying components denoting trend, various oscillatory components and noise components.
The WavSD for TradingSolutions product works similarly to Jurik Indicators WAV and
DDR for TradingSolutions, but without the requirement of Jurik Indicators.
What is WavSD for TradingSolutions?
WavSD is a complex data processing algorithm executed in two distinct steps. The first step is the embedding step performed by the Native Wav sampler, in which the onedimensional time
series (for instance daily closing price of a security) is represented as multidimensional trajectory matrix of sampled data characterized only by a particular timewindow length. The second step is the
Spectral Decomposition of the trajectory matrix into a sum of orthogonal matrices, resulting in a number of new columns of decorrelated data with descending information content. WavSD algorithm
assumes no prior knowledge about the analyzed data, it is completely automatic and no user input of any kind is necessary. In addition to sampling, detrending, normalizing and decorrelating data, the
WavSD for Trading Solutions enables users to optimize the sampled data timeframe, making it the ultimate data preprocessing solution designed to perform spatiotemporal compression of market data very
effectively.
This very powerful concept will provide meaningful data for your models and very likely enhance model’s performance and robustness.
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WavSD Chart in TradingSolutions
The advanced indicators in this addon do not easily fit within the TradingSolutions framework due to the fact they produce arrays or matrices of data and for this purpose a custom external engine was
built. The design of the addon is modular, providing numerous options for combining and optimizing data preprocessing. The external engine is very fast and made as transparent for the user as possible.
Additionally, a separate database maintenance tool is included.
Native Wav  Wavelet Sampling Filter
Native Wav algorithm maps the original time series to a sequence of multidimensional lagged vectors from by automatically adding columns of values derived from calculations applied to input data.
The number of lagged vectors is determined by the sampled window length, i.e. the desired lookback period input by the user. The ultimate result is the reduction of the data required to represent
the sampled time window  temporal compression. Proper forecasting usually requires the raw data to be detrended and/or normalized before further processing. Native Wav offers the user these options
and will preprocess data automatically.
Native Wav Chart in TradingSolutions
SD  Spectral Decomposition
SD algorithm analyzes the array of the selected starting indicators and produces a transformation matrix which is then used to produce a new array of data exactly the same size as the original.
However, each column in the new array is 100% decorrelated from all others, and they are arranged according to their information content, from the most informative columns to the least informative.
This algorithm is intended to be used on the matrices of lagged vectors produced by Native Wav sampler but can be applied to any data array. This performs additional compression of data by
eliminating all redundancy contained in the original data.
SD Chart in TradingSolutions
Applications of WavSD for TradingSolutions
The applications for use of SD, WavSD and Native Wav in TradingSolutions are nearly limitless! It can be used for neural network modeling or system development, data filtering and advanced technical analysis.
In the "View More" below you will find examples of each application and how WavSD can bring in a new level of advanced analysis into TradingSolutions.
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Model/System Development
The properties of WavSD outputs (high data content with reduced noise and mutual decorrelation) make them ideal for model/system development. The following example shows a simple system based on the 139sample
period WavSD of the Ford Motor Credit Co. (NASDAQ: F) closing price. The system uses the first WavSD output predicted 5 samples in advance. The system enters long or short whenever the difference of the predicted
WavSD output from its moving average crosses above or below a threshold and a simple 1% trailing stop was added. This system outperforms the buy/hold strategy by 106% in the period from from January 28, 2011
to January 28, 2012.


Ford WavSD Signals

Ford Equity Curve

Alternatively, the WavSD outputs can be fed directly into a neural network model. This example uses the WavSD of the Ford Motor Credit Co (NASDAQ: F) closing price in the default TimeLagged Recurrent Network
and Optimal Signal. The resulting system yields a 78% return over the buy/hold strategy in the out of sample period from June 15, 2011 to January 28, 2012.


Ford WavSD Model Signals

Ford Equity Curve

Data Filtering
Using WavSD outputs for Apple Inc. (NASDAQ: AAPL) closing price to build a neural network price proxy model. The model is 88.1% accurate, but much of the noise has been filtered and no lag has been introduced.
The target for the neural network (and the input for the WavSD analysis) was the detrended and normalized closing price, processed by the Native Wav function.


(Red) Closing Price vs. (Green) Native Wav function

3 WavSD Inputs

All important information necessary for the reconstruction of input data is contained in these three outputs of WavSD, displayed below. The first output denotes the major trend component, whereas the
subsequent outputs are various oscillatory components of the original data. WavSD makes absolutely no assumptions on the underlying data and the only user input parameters is the lookback period, the
detrend or detrend/normalize flags and a number of desired output columns.
Data Prediction
WavSD outputs are usually smooth, normalized oscillators, particularly suitable for neural network modeling, either as inputs or as target outputs. This example shows the WavSD of the closing price for
Oracle Corp. (NASDAQ: ORCL) predicted 5 samples in advance. The network output is a leading indicator 95% correlated to the desired putput and anticipates its major movements.
Data Prediction using WavSD
Advanced Technical Analysis
WavSD outputs can also be used for technical analysis. Inthis example, a stochastic oscillator (%K) based on the closing price of CocaCola Co. (NYSE: KO) can be compared to the one based on the first output
of the WavSD of the closing price. Both oscillators successfully capture trends in the original data but the latter clearly benefits from the smoother input of the WavSD preprocessed data. Similar
improvements should be observed for any technical indicator ordinarily plagued by the inherit noise in market data.
Advanced Technical Analysis using WavSD
How Does WavSD Compare to Jurik with WavDDR?
WavSD for TradingSolutions provides similar results when compared to Jurik Indicators for a fraction of the cost!


(Top) WavSD Outputs (Bottom) Jurik WavDDR Outputs

(Top) Model based on WavSD (Bottom) Model based on Jurik WavDDR

How to Order
The WavSD for TradingSolutions addon may be purchased directly on our website through the Secure Online Order Form.
