Applications of Signal Processing in Finance

Vishrant Tripathi, Jitesh Gosar, Hemendra Meena and Grandhi Srujan

Electrical Engineering Department, IIT-Bombay

March 20,2016

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Overview

1 IntroductionIs Signal Processing Useful in Analyzing Financial Data?FilteringProblems with conventional DSP

2 Algorithmic TradingCausal Modeling

3 Empirical Mode DecompositionTime-frequency representationsEMDSynchro-Squeezing TransformExamples

4 Conclusion

5 References

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Introduction

Finance and economy developed for centuries without reference toadvanced mathematics (and signal processing).

The pioneering work of Fischer Black and Myron Scholes changed allthat.[5]

The mathematization of the financial system places policy making inthe hands of the experts and increases investors’ trust

Decisions are directly based on realistic, observable, and reproduciblequantitative analysis instead of the ”good hunch” of a ”market-seasoned veteran”

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Is Signal Processing Useful in Analyzing Financial Data?

Signal processing techniques play an important role in today’sfinances.

These techniques are used to represent and predict the main featuresof price evolution and to classify stock so as to design diversifiedinvestment

Monitoring the price of the financial products and extrapolating theirfuture evolution according to past available information can be viewedas a classical signal processing problem.

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Filtering

Financial time-series data often consists of long-term trends in the presence ofhigh-frequency and wildly fluctuating noise. Thus, simple techniques likemoving-average filters, and low-pass filters are usually employed to first removethis noise from the signals, before moving on to the actual processing ofwaveforms. Advanced methods like adaptive Kalman filters are also used in somecases for removal of noise and extracting meaningful information.

Figure: Trend line obtained by filtering

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Problems with conventional DSP

Figure: For two signals which are quite different in the time domain, we observealmost same spectra, thus motivating the need for time-frequency analysis

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Problems with conventional DSP

Most concepts of signal processing that we have learnt during thecourse work well with stationary signals - signals whose power spectraldensity is constant with time.

However financial time-series data is highly non-stationary in nature,due to wild and often unpredictable fluctuations.

We are exploring a new technique that aims to tackle some of theseproblems while still being computationally efficient - theSynchro-Squeezing Transform.

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Algorithmic Trading

Trading a financial instrument by forecasting its future value based onsome algorithm

Subjective forecasting

is performed based on experience, intuition and guesswork. It is usuallyinferred from both macroeconomic and microeconomic factors

Extrapolation techniques

whose aim is to project past trends into the future. Common extrapolationtechniques include regression analysis and methods based on error criteria,such as the mean absolute deviation and the mean squared error

Causal modeling

where the goal is to predict a lagging variable based on a leading variable.The relationship between these two variables can be modeled as a causeand effect

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Causal Modeling

For a forecasting technique to be useful, it must add information towhat is already known: the main issue is how to take advantage ofthis lead-lag relationship to perform prediction.

In this spirit, authors of [1] have proposed a real-time tradingalgorithm that exploits the lead-lag relationship between a pair ofstock prices to forecast the price of the lagging asset

This is achieved by using the recently proposed SynchrosqueezedTransform to quantify the lead-lag relationship

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Time-frequency representations

Time-frequency representations provide a powerful tool for theanalysis of time series signals and give insight into the complexstructure of multi-layered signals

Examples are the windowed Fourier transform, where the family oftemplates is generated by translating and modulating a basic windowfunction, or the wavelet transform, where the templates are obtainedby translating and dilating the basic wavelet

Heisenberg uncertainty principle limits the resolution that can beattained in the TF plane

Such representations are often not useful for wildly fluctuating signals

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Empirical mode Decomposition

The Empirical Mode Decomposition (EMD) method was proposed by NordenHuang as an algorithm that would allow time-frequency analysis of suchmulticomponent signals, without the weaknesses sketched above, overcoming inparticular artificial spectrum spread caused by sudden changes. A signal is brokendown into Intrinsic Mode Functions (IMFs)

Figure: EMD

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Synchro-Squeezing Transform

Synchrosqueezing was introduced in the context of analyzing auditorysignals ; it is a special case of reallocation methods which aim to sharpena time-frequency representation R(t,w) by allocating its value to adifferent point (t1, w1) ) in the time-frequency plane, determined by thelocal behavior of R(t, w) around (t, w). One starts from the continuouswavelet transform Ws of the signal s(t) defined by

Theorem (Continuous Wavelet Transform)

Ws =∫s(t)a−1/2ψ( t−b

a )dt

and then reallocates the Ws(a, b) to get a concentrated time-frequencypicture, from which instantaneous frequency lines can be extracted

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Examples

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Examples

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Examples

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Examples

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Conclusion

We conclude that the Synchro-Squeezing Transform provides a veryelegant and useful way to analyze non-stationary time-series data andis often better suited to applications in finance as compared to theregular CWT, DWT or STFT procedures.

Also, the ability to extract long term phase relationship of signalsaccurately in the presence of noise makes this transform particularlywell suited to applications in algorithmic trading based on causalmodeling.

For financial products with a known lead-lag relationship, phase andsynchronization information can be extracted using this approach forforecasting and making decisions. This has been verified for a largevariety of stocks in [2].

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References

Application of Signal Processing to the Analysis of Financial Data -

Konstantinos Drakakis, IEEE SIGNAL PROCESSING MAGAZINE [157]SEPTEMBER 2009

Algorithmic Trading Using Phase Synchronization -

A. Ahrabian, C. C. Took, and D. P. Mandic - IEEE JOURNAL OF SELECTEDTOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 4, AUGUST 2012

Introduction to the Issue on Signal Processing Methods in Finance and ElectronicTrading -

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6,NO. 4, AUGUST 2012

Applications of HilbertHuang transform to non-stationary financial time seriesanalysis -

N. E. Huang, M. Wu , W. Qu, S. Long, S. P. Shen and Jin Zhang - Appl.Stochastic Models Bus. Ind., 2003; 19:361 (DOI: 10.1002/asmb.506)

Synchrosqueezed Wavelet Transforms: an Empirical Mode Decomposition-like Tool

Ingrid Daubechies, Jianfeng Lu1, Hau-Tieng Wu Department of Mathematics andProgram in Applied and Computational Mathematics Princeton University,Princeton, NJ, 08544

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The End

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