Applications of Signal Processing in Finance

Transcription

1 Applications of Signal Processing in Finance Vishrant Tripathi, Jitesh Gosar, Hemendra Meena and Grandhi Srujan Electrical Engineering Department, IIT-Bombay March 20,2016 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

2 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

3 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 marketseasoned veteran Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

4 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. Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

5 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

6 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

7 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. Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

8 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

9 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

10 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

11 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 Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

12 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) W s = s(t)a 1/2 ψ( t b a )dt and then reallocates the Ws(a, b) to get a concentrated time-frequency picture, from which instantaneous frequency lines can be extracted Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

13 Examples Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

14 Examples Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

15 Examples Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

16 Examples Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

17 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]. Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19

18 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, Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19 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: /asmb.506)

19 The End Vishrant, Jitesh, Hemendra & Srujan (IITB) DSP in Finance March 20, / 19