ELEC70103 Signal Processing and Machine Learning for FinanceLecturer(s): Prof Danilo Mandic Aims
Traditional mathematical approaches in finance data modelling and information extraction are based on stochastic calculus and econometrics, which by and large enforce probabilistic models on observed data. However, with the rapid changes the global financial system is undergoing, financial models need to be adaptively inferred from the data, the approach taken in this course. This requires expertise in Data Analytics areas, as exemplified by the fact that between 6080% of trading is currently performed by algorithms which run on machines, with signal processing and machine learning as the underpinning technologies. By treating the financial data as arising from a nonstationary multivariate dynamic system, and by identifying and exploiting numerous dualities between Finance and Data Analytics (e.g. Sharpe ratio vs signal to noise ratio, mean variance portfolio vs adaptive beamformer), DSP and ML techniques offer both additional rigour in the understanding and interpretation and real time mode of operation. The approach will be based on the evolution of concepts, in a step by step fashion, from single assets (univariate model), to portfolios (multiple assets, multivariate problem), to asset allocation and wealth maximization (big data and machine learning problem).
Fundamental to the whole course is the examination of financial data and relevant methods based on the solid frameworks of signal processing and machine learning. This course is driven by time series perspectives and short term statistical behaviour, underpinned by digital signal processing and machine learning, which is appropriate for cash assets (stocks, bonds and currencies) and futures. It therefore answers the needs of the rapidly changing global financial system which requires financial models to be adaptively inferred from the data. Learning Outcomes
1. Knowledge and understanding:
 Understanding of finance, qualitative and quantitative principles and methodologies, based on signal processing and machine learning techniques.  Understanding of the scientific foundations of finance, and being exposed to relevant historical, current and future approaches to economic and financial problems.  Knowledge and understanding of the fundamental economic drivers of the financial markets and behavioural economics, and awareness of their relevance to successful trading algorithms.  A thorough understanding of current practice and limitations of the methodologies used to model financial data, and the ability to identify and evaluate suitable models for different types of markets and investment strategies.  Understanding the different stages within the investment process and strategy development workflow.  Knowledge and understanding of risk issues with current financial models and portfolio optimisation methods. 2. Subject Specific Skills and other attributes: a) Intellectual skills:  Ability to investigate and apply the mathematical and statistical methods within DSP and ML disciplines to forecast, analyse and interpret the nonlinear and nonstationary relationships within large baskets of financial assets, the ability to evaluate the results critically, and to apply the models effectively in the solution of unfamiliar problems.  Engage in curiosity driven learning and explore feasible extensions and new applications of their taught material.  Enhance their creativity both in learning and applying the concepts with the additional “opportunity windows” to explore possible product developments. b) Practical Skills:  Ability to apply quantitative and computational methods using alternative approaches and understanding their limitations, in order to solve problems and implement appropriate action within the context of data analysis, forecasting, portfolio optimisation and risk management.  Ability to identify, classify and assess the performance of financial models through the use of analytical methods and risk modelling techniques.  Ability to use fundamental knowledge to investigate new and emerging technologies for financial applications.  A number of Case Studies (see the Syllabus) are carefully designed to fully reflect the relevance of the material taught in the course, and to and further empower the students with enhanced intuition and freedom in algorithmic design. c) Transferable / Key Skills:  Ability to work with technical uncertainty.  The students will be able to understand sophisticated techniques for systematic and algorithmic trading and to evaluate current approaches in finance. Awareness of developing technologies related to DSP and ML from a range of areas outside the context of finance, and the ability to evaluate them critically and to apply them effectively in financial contexts.  Experience that difficulties in realworld signal analysis are surmountable. Syllabus
Part 1: Preliminaries
1.1. Introduction: Background, general definitions and objectives Econometrics and financial engineering, commonalities and differences with signal processing and machine learning. Definitions of an asset, asset returns basics, variance and covariance. Definition of stocks. Introduction to classic behavioural finance theory (Efficient Market Theory), its limitations and modern theories (Adaptive Market Hypothesis), the digital signal processing underpinning for these (deterministic vs stochastic signals and stationary vs nonstationary signals). 1.2. Advanced least squares methods: High dimensional vector spaces Estimation of vector space bases from real data, their interpretation as market regimes, mean square error based estimation, low rank approximation and reduced vector spaces, recursive estimation. Part 2: Data science for financial analysis 2.1 Dealing with nonstationarity: Trends, measures of (non) stationarity Assets and seasonality, trend line and cointegration. 2.2 Time series approaches Role of memory in modelling, ARIMA(p,d,q) for directional models, vector autoregressive (VAR) models for cointegration, model order selection, volatility detection and estimation, from a single univariate asset via a multivariate stock to a tensorvalued portfolio. 2.3 Robust and nonlinear models Nonlinearities in the market signals, Jensen’s inequality and hidden higherorder risks (convexity), universal approximation, nonlinear eigenvalue problems, data sample size and implications, nonGaussian distributions and fat tails, robust statistics Part 3: Model dependent approaches 3.1. Model based Data Analytics General framework for statistical factor analysis, asset returns, macroeconomic factor models, factor model of Sharpe, crosssectional regression, conditional volatility models, ARCH and GARCH, testing of GARCH models, normality, linear factor models and time series, discount dividend model, NPV (net present value), why deep models matter. 3.2. Portfolio selection: Asset pricing signal processing and estimation Risk modelling and estimation, measures of asset risk, CAPM and APT, discount dividend model, efficient frontier and returnrisk relationship, robust principal component analysis. 3.3. Techniques for portfolio optimisation: Performance maximisation Active and factor returns, alpha forecasting, expected returns, Markowitz portfolio, statistical cointegration vs correlation (meanvariance constrained optimisation), performance ratios (Sharpe, Sortino, ValueatRisk, Expected Shortfall, Drawdown), realtime covariance estimation, adaptive direction method of multipliers (ADMM) for realtime optimisation, duality with DSP and ML . Part 4: Machine Intelligence methods 4.1. Predictive machine learning techniques: Dynamical assignment of features Choice of appropriate ML method, point estimation vs probabilistic estimation, penalised regression models (LASSO, ridge, elastic nets), constrained models, kernel based methods and clustering, curse of dimensionality, quality measures in forecasting. 4.2. Big data in finance: Dimensionality reduction and latent component analysis. Multiway data structures, from SVD to Tucker decomposition, from SVM to support tensor machine, applications (futures, markets and pricing), crossportfolio modelling. 4.3 Graph theory for finance: Signals on graphs, regression on graphs, graph machine learning algorithms, Big Data on graphs, finding cliques, correlated cliques, correlated portfolio, robustification of portfolios through graphs, from graph theory to models of economic networks. Examination: This is a 100% Coursework module Exam Duration: N/A Coursework contribution: 100% Term: Spring Closed or Open Book (end of year exam): N/A Coursework Requirement: Coursework only module Oral Exam Required (as final assessment): N/A Prerequisite module(s): None required Course Homepage: https://bb.imperial.ac.uk Book List:
