Advances in financial machine learning

Intro -- Advances in Financial Machine Learning -- Contents -- About the Author -- Preamble -- 1 Financial Machine Learning as a Distinct Subject -- 1.1 Motivation -- 1.2 The Main Reason Financial Machine Learning Projects Usually Fail -- 1.2.1 The Sisyphus Paradigm -- 1.2.2 The Meta-Strategy Paradigm -- 1.3 Book Structure -- 1.3.1 Structure by Production Chain -- 1.3.2 Structure by Strategy Component -- 1.3.3 Structure by Common Pitfall -- 1.4 Target Audience -- 1.5 Requisites -- 1.6 FAQs -- 1.7 Acknowledgments -- Exercises -- References -- Bibliography -- PART 1 Data Analysis -- 2 Financial Data Structures -- 2.1 Motivation -- 2.2 Essential Types of Financial Data -- 2.2.1 Fundamental Data -- 2.2.2 Market Data -- 2.2.3 Analytics -- 2.2.4 Alternative Data -- 2.3 Bars -- 2.3.1 Standard Bars -- 2.3.2 Information-Driven Bars -- 2.4 Dealing with Multi-Product Series -- 2.4.1 The ETF Trick -- 2.4.2 PCA Weights -- 2.4.3 Single Future Roll -- 2.5 Sampling Features -- 2.5.1 Sampling for Reduction -- 2.5.2 Event-Based Sampling -- Exercises -- References -- 3 Labeling -- 3.1 Motivation -- 3.2 The Fixed-Time Horizon Method -- 3.3 Computing Dynamic Thresholds -- 3.4 The Triple-Barrier Method -- 3.5 Learning Side and Size -- 3.6 Meta-Labeling -- 3.7 How to Use Meta-Labeling -- 3.8 The Quantamental Way -- 3.9 Dropping Unnecessary Labels -- Exercises -- Bibliography -- 4 Sample Weights -- 4.1 Motivation -- 4.2 Overlapping Outcomes -- 4.3 Number of Concurrent Labels -- 4.4 Average Uniqueness of a Label -- 4.5 Bagging Classifiers and Uniqueness -- 4.5.1 Sequential Bootstrap -- 4.5.2 Implementation of Sequential Bootstrap -- 4.5.3 A Numerical Example -- 4.5.4 Monte Carlo Experiments -- 4.6 Return Attribution -- 4.7 Time Decay -- 4.8 Class Weights -- Exercises -- References -- Bibliography -- 5 Fractionally Differentiated Features -- 5.1 Motivation

5.2 The Stationarity vs. Memory Dilemma -- 5.3 Literature Review -- 5.4 The Method -- 5.4.1 Long Memory -- 5.4.2 Iterative Estimation -- 5.4.3 Convergence -- 5.5 Implementation -- 5.5.1 Expanding Window -- 5.5.2 Fixed-Width Window Fracdiff -- 5.6 Stationarity with Maximum Memory Preservation -- 5.7 Conclusion -- Exercises -- References -- Bibliography -- PART 2 Modelling -- 6 Ensemble Methods -- 6.1 Motivation -- 6.2 The Three Sources of Errors -- 6.3 Bootstrap Aggregation -- 6.3.1 Variance Reduction -- 6.3.2 Improved Accuracy -- 6.3.3 Observation Redundancy -- 6.4 Random Forest -- 6.5 Boosting -- 6.6 Bagging vs. Boosting in Finance -- 6.7 Bagging for Scalability -- Exercises -- References -- Bibliography -- 7 Cross-Validation in Finance -- 7.1 Motivation -- 7.2 The Goal of Cross-Validation -- 7.3 Why K-Fold CV Fails in Finance -- 7.4 A Solution: Purged K-Fold CV -- 7.4.1 Purging the Training Set -- 7.4.2 Embargo -- 7.4.3 The Purged K-Fold Class -- 7.5 Bugs in Sklearns Cross-Validation -- Exercises -- Bibliography -- 8 Feature Importance -- 8.1 Motivation -- 8.2 The Importance of Feature Importance -- 8.3 Feature Importance with Substitution Effects -- 8.3.1 Mean Decrease Impurity -- 8.3.2 Mean Decrease Accuracy -- 8.4 Feature Importance without Substitution Effects -- 8.4.1 Single Feature Importance -- 8.4.2 Orthogonal Features -- 8.5 Parallelized vs. Stacked Feature Importance -- 8.6 Experiments with Synthetic Data -- Exercises -- References -- 9 Hyper-Parameter Tuning with Cross-Validation -- 9.1 Motivation -- 9.2 Grid Search Cross-Validation -- 9.3 Randomized Search Cross-Validation -- 9.3.1 Log-Uniform Distribution -- 9.4 Scoring and Hyper-parameter Tuning -- Exercises -- References -- Bibliography -- PART 3 Backtesting -- 10 Bet Sizing -- 10.1 Motivation -- 10.2 Strategy-Independent Bet Sizing Approaches

10.3 Bet Sizing from Predicted Probabilities -- 10.4 Averaging Active Bets -- 10.5 Size Discretization -- 10.6 Dynamic Bet Sizes and Limit Prices -- Exercises -- References -- Bibliography -- 11 The Dangers of Backtesting -- 11.1 Motivation -- 11.2 Mission Impossible: The Flawless Backtest -- 11.3 Even If Your Backtest Is Flawless, It Is Probably Wrong -- 11.4 Backtesting Is Not a Research Tool -- 11.5 A Few General Recommendations -- 11.6 Strategy Selection -- Exercises -- References -- Bibliography -- 12 Backtesting through Cross-Validation -- 12.1 Motivation -- 12.2 The Walk-Forward Method -- 12.2.1 Pitfalls of the Walk-Forward Method -- 12.3 The Cross-Validation Method -- 12.4 The Combinatorial Purged Cross-Validation Method -- 12.4.1 Combinatorial Splits -- 12.4.2 The Combinatorial Purged Cross-Validation Backtesting Algorithm -- 12.4.3 A Few Examples -- 12.5 How Combinatorial Purged Cross-Validation Addresses Backtest Overfitting -- Exercises -- References -- 13 Backtesting on Synthetic Data -- 13.1 Motivation -- 13.2 Trading Rules -- 13.3 The Problem -- 13.4 Our Framework -- 13.5 Numerical Determination of Optimal Trading Rules -- 13.5.1 The Algorithm -- 13.5.2 Implementation -- 13.6 Experimental Results -- 13.6.1 Cases with Zero Long-Run Equilibrium -- 13.6.2 Cases with Positive Long-Run Equilibrium -- 13.6.3 Cases with Negative Long-Run Equilibrium -- 13.7 Conclusion -- Exercises -- References -- 14 Backtest Statistics -- 14.1 Motivation -- 14.2 Types of Backtest Statistics -- 14.3 General Characteristics -- 14.4 Performance -- 14.4.1 Time-Weighted Rate of Return -- 14.5 Runs -- 14.5.1 Returns Concentration -- 14.5.2 Drawdown and Time under Water -- 14.5.3 Runs Statistics for Performance Evaluation -- 14.6 Implementation Shortfall -- 14.7 Efficiency -- 14.7.1 The Sharpe Ratio -- 14.7.2 The Probabilistic Sharpe Ratio

14.7.3 The Deflated Sharpe Ratio -- 14.7.4 Efficiency Statistics -- 14.8 Classification Scores -- 14.9 Attribution -- Exercises -- References -- Bibliography -- 15 Understanding Strategy Risk -- 15.1 Motivation -- 15.2 Symmetric Payouts -- 15.3 Asymmetric Payouts -- 15.4 The Probability of Strategy Failure -- 15.4.1 Algorithm -- 15.4.2 Implementation -- Exercises -- References -- 16 Machine Learning Asset Allocation -- 16.1 Motivation -- 16.2 The Problem with Convex Portfolio Optimization -- 16.3 Markowitzs Curse -- 16.4 From Geometric to Hierarchical Relationships -- 16.4.1 Tree Clustering -- 16.4.2 Quasi-Diagonalization -- 16.4.3 Recursive Bisection -- 16.5 A Numerical Example -- 16.6 Out-of-Sample Monte Carlo Simulations -- 16.7 Further Research -- 16.8 Conclusion -- APPENDICES -- 16.A.1 Correlation-based Metric -- 16.A.2 Inverse Variance Allocation -- 16.A.3 Reproducing the Numerical Example -- 16.A.4 Reproducing the Monte Carlo Experiment -- Exercises -- References -- PART 4 Useful Financial Features -- 17 Structural Breaks -- 17.1 Motivation -- 17.2 Types of Structural Break Tests -- 17.3 CUSUM Tests -- 17.3.1 Brown-Durbin-Evans CUSUM Test on Recursive Residuals -- 17.3.2 Chu-Stinchcombe-White CUSUM Test on Levels -- 17.4 Explosiveness Tests -- 17.4.1 Chow-Type Dickey-Fuller Test -- 17.4.2 Supremum Augmented Dickey-Fuller -- 17.4.3 Sub- and Super-Martingale Tests -- Exercises -- References -- 18 Entropy Features -- 18.1 Motivation -- 18.2 Shannons Entropy -- 18.3 The Plug-in (or Maximum Likelihood) Estimator -- 18.4 Lempel-Ziv Estimators -- 18.5 Encoding Schemes -- 18.5.1 Binary Encoding -- 18.5.2 Quantile Encoding -- 18.5.3 Sigma Encoding -- 18.6 Entropy of a Gaussian Process -- 18.7 Entropy and the Generalized Mean -- 18.8 A Few Financial Applications of Entropy -- 18.8.1 Market Efficiency -- 18.8.2 Maximum Entropy Generation

18.8.3 Portfolio Concentration -- 18.8.4 Market Microstructure -- Exercises -- References -- Bibliography -- 19 Microstructural Features -- 19.1 Motivation -- 19.2 Review of the Literature -- 19.3 First Generation: Price Sequences -- 19.3.1 The Tick Rule -- 19.3.2 The Roll Model -- 19.3.3 High-Low Volatility Estimator -- 19.3.4 Corwin and Schultz -- 19.4 Second Generation: Strategic Trade Models -- 19.4.1 Kyles Lambda -- 19.4.2 Amihuds Lambda -- 19.4.3 Hasbroucks Lambda -- 19.5 Third Generation: Sequential Trade Models -- 19.5.1 Probability of Information-based Trading -- 19.5.2 Volume-Synchronized Probability of Informed Trading -- 19.6 Additional Features from Microstructural Datasets -- 19.6.1 Distibution of Order Sizes -- 19.6.2 Cancellation Rates, Limit Orders, Market Orders -- 19.6.3 Time-Weighted Average Price Execution Algorithms -- 19.6.4 Options Markets -- 19.6.5 Serial Correlation of Signed Order Flow -- 19.7 What Is Microstructural Information? -- Exercises -- References -- PART 5 High-Performance Computing Recipes -- 20 Multiprocessing and Vectorization -- 20.1 Motivation -- 20.2 Vectorization Example -- 20.3 Single-Thread vs. Multithreading vs. Multiprocessing -- 20.4 Atoms and Molecules -- 20.4.1 Linear Partitions -- 20.4.2 Two-Nested Loops Partitions -- 20.5 Multiprocessing Engines -- 20.5.1 Preparing the Jobs -- 20.5.2 Asynchronous Calls -- 20.5.3 Unwrapping the Callback -- 20.5.4 Pickle/Unpickle Objects -- 20.5.5 Output Reduction -- 20.6 Multiprocessing Example -- Exercises -- Reference -- Bibliography -- 21 Brute Force and Quantum Computers -- 21.1 Motivation -- 21.2 Combinatorial Optimization -- 21.3 The Objective Function -- 21.4 The Problem -- 21.5 An Integer Optimization Approach -- 21.5.1 Pigeonhole Partitions -- 21.5.2 Feasible Static Solutions -- 21.5.3 Evaluating Trajectories -- 21.6 A Numerical Example

21.6.1 Random Matrices

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Includes index