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 Introduction
Is Signal Processing Useful in Analyzing Financial Data?
Filtering
Problems with conventional DSP
2 Algorithmic Trading
Causal Modeling
3 Empirical Mode Decomposition
Time-frequency representations
EMD
Synchro-Squeezing Transform
Examples
4 Conclusion
5 References
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Introduction
Finance and economy developed for centuries without reference to
advanced mathematics (and signal processing).
The pioneering work of Fischer Black and Myron Scholes changed all
that.[5]
The mathematization of the financial system places policy making in
the hands of the experts and increases investors’ trust
Decisions are directly based on realistic, observable, and reproducible
quantitative 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’s
finances.
These techniques are used to represent and predict the main features
of price evolution and to classify stock so as to design diversified
investment
Monitoring the price of the financial products and extrapolating their
future evolution according to past available information can be viewed
as a classical signal processing problem.
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Filtering
Financial time-series data often consists of long-term trends in the presence of
high-frequency and wildly fluctuating noise. Thus, simple techniques like
moving-average filters, and low-pass filters are usually employed to first remove
this noise from the signals, before moving on to the actual processing of
waveforms. Advanced methods like adaptive Kalman filters are also used in some
cases 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 observe
almost 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 the
course work well with stationary signals - signals whose power spectral
density 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 these
problems while still being computationally efficient - the
Synchro-Squeezing Transform.
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Algorithmic Trading
Trading a financial instrument by forecasting its future value based on
some algorithm
Subjective forecasting
is performed based on experience, intuition and guesswork. It is usually
inferred from both macroeconomic and microeconomic factors
Extrapolation techniques
whose aim is to project past trends into the future. Common extrapolation
techniques 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 cause
and effect
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Causal Modeling
For a forecasting technique to be useful, it must add information to
what is already known: the main issue is how to take advantage of
this lead-lag relationship to perform prediction.
In this spirit, authors of [1] have proposed a real-time trading
algorithm that exploits the lead-lag relationship between a pair of
stock prices to forecast the price of the lagging asset
This is achieved by using the recently proposed Synchrosqueezed
Transform to quantify the lead-lag relationship
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Time-frequency representations
Time-frequency representations provide a powerful tool for the
analysis of time series signals and give insight into the complex
structure of multi-layered signals
Examples are the windowed Fourier transform, where the family of
templates is generated by translating and modulating a basic window
function, or the wavelet transform, where the templates are obtained
by translating and dilating the basic wavelet
Heisenberg uncertainty principle limits the resolution that can be
attained 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 Norden
Huang as an algorithm that would allow time-frequency analysis of such
multicomponent signals, without the weaknesses sketched above, overcoming in
particular artificial spectrum spread caused by sudden changes. A signal is broken
down into Intrinsic Mode Functions (IMFs)
Figure: EMD
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Synchro-Squeezing Transform
Synchrosqueezing was introduced in the context of analyzing auditory
signals ; it is a special case of reallocation methods which aim to sharpen
a time-frequency representation R(t,w) by allocating its value to a
different point (t1, w1) ) in the time-frequency plane, determined by the
local behavior of R(t, w) around (t, w). One starts from the continuous
wavelet transform Ws of the signal s(t) defined by
Theorem (Continuous Wavelet Transform)
s(t)a−1/2 ψ( t−b
R
Ws = a )dt
and then reallocates the Ws(a, b) to get a concentrated time-frequency
picture, 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 very
elegant and useful way to analyze non-stationary time-series data and
is often better suited to applications in finance as compared to the
regular CWT, DWT or STFT procedures.
Also, the ability to extract long term phase relationship of signals
accurately in the presence of noise makes this transform particularly
well suited to applications in algorithmic trading based on causal
modeling.
For financial products with a known lead-lag relationship, phase and
synchronization information can be extracted using this approach for
forecasting and making decisions. This has been verified for a large
variety 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 SELECTED
TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 4, AUGUST 2012
Introduction to the Issue on Signal Processing Methods in Finance and Electronic
Trading -
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6,
NO. 4, AUGUST 2012
Applications of HilbertHuang transform to non-stationary financial time series
analysis -
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 and
Program in Applied and Computational Mathematics Princeton University,
Princeton, NJ, 08544
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The End
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