Preface xvii About the Authors xxiii Part One Language Fundamentals Chapter 1 Fundamentals of the q Programming Language 3 1.1 The (Not So Very) First Steps in q 3 1.2 Atoms and Lists 5 1.2.1 Casting Types 11 1.3 Basic Language Constructs 14 1.3.1 Assigning, Equality and Matching 14 1.

3.2 Arithmetic Operations and Right-to-Left Evaluation: Introduction to q Philosophy 17 1.4 Basic Operators 19 1.5 Difference between Strings and Symbols 31 1.5.1 Enumeration 31 1.6 Matrices and Basic Linear Algebra in q 33 1.7 Launching the Session: Additional Options 35 1.

8 Summary and How-To''s 38 Chapter 2 Dictionaries and Tables: The q Fundamentals 41 2.1 Dictionary 41 2.2 Table 44 2.3 The Truth about Tables 48 2.4 Keyed Tables are Dictionaries 50 2.5 From a Vector Language to an Algebraic Language 51 Chapter 3 Functions 57 3.1 Namespace 59 3.1.

0.1 .quantQ. Namespace 60 3.2 The Six Adverbs 60 3.2.1 Each 60 3.2.

1.1 Each 61 3.2.1.2 Each-left \: 61 3.2.1.3 Each-right /: 62 3.

2.1.4 Cross Product /: \: 62 3.2.1.5 Each-both '' 63 3.2.2 Each-prior '': 66 3.

2.3 Compose ('') 67 3.2.4 Over and Fold / 67 3.2.5 Scan 68 3.2.5.

1 EMA: The Exponential Moving Average 69 3.2.6 Converge 70 3.2.6.1 Converge-repeat 70 3.2.6.

2 Converge-iterate 71 3.3 Apply 72 3.3.1 @ (apply) 72 3.3.2 . (apply) 73 3.4 Protected Evaluations 75 3.

5 Vector Operations 76 3.5.1 Aggregators 76 3.5.1.1 Simple Aggregators 76 3.5.1.

2 Weighted Aggregators 77 3.5.2 Uniform Functions 77 3.5.2.1 Running Functions 77 3.5.2.

2 Window Functions 78 3.6 Convention for User-Defined Functions 79 Chapter 4 Editors and Other Tools 81 4.1 Console 81 4.2 Jupyter Notebook 82 4.3 GUIs 84 4.3.1 qStudio 85 4.3.

2 Q Insight Pad 88 4.4 IDEs: IntelliJ IDEA 90 4.5 Conclusion 92 Chapter 5 Debugging q Code 93 5.1 Introduction to Making It Wrong: Errors 93 5.1.1 Syntax Errors 94 5.1.2 Runtime Errors 94 5.

1.2.1 The Type Error 95 5.1.2.2 Other Errors 98 5.2 Debugging the Code 100 5.3 Debugging Server-Side 102 Part Two Data Operations Chapter 6 Splayed and Partitioned Tables 107 6.

1 Introduction 107 6.2 Saving a Table as a Single Binary File 108 6.3 Splayed Tables 110 6.4 Partitioned Tables 113 6.5 Conclusion 119 Chapter 7 Joins 121 7.1 Comma Operator 121 7.2 Join Functions 125 7.2.

1 ij 125 7.2.2 ej 126 7.2.3 lj 126 7.2.4 pj 127 7.2.

5 upsert 128 7.2.6 uj 129 7.2.7 aj 131 7.2.8 aj0 134 7.2.

8.1 The Next Valid Join 135 7.2.9 asof 138 7.2.10 wj 140 7.3 Advanced Example: Running TWAP 144 Chapter 8 Parallelisation 151 8.1 Parallel Vector Operations 152 8.

2 Parallelisation over Processes 155 8.3 Map-Reduce 155 8.4 Advanced Topic: Parallel File/Directory Access 158 Chapter 9 Data Cleaning and Filtering 161 9.1 Predicate Filtering 161 9.1.1 The Where Clause 161 9.1.2 Aggregation Filtering 163 9.

2 Data Cleaning, Normalising and APIs 163 Chapter 10 Parse Trees 165 10.1 Definition 166 10.1.1 Evaluation 166 10.1.2 Parse Tree Creation 170 10.1.3 Read-Only Evaluation 170 10.

2 Functional Queries 171 10.2.1 Functional Select 174 10.2.2 Functional Exec 178 10.2.3 Functional Update 179 10.2.

4 Functional Delete 180 Chapter 11 A Few Use Cases 181 11.1 Rolling VWAP 181 11.1.1 N Tick VWAP 181 11.1.2 TimeWindow VWAP 182 11.2 Weighted Mid for N Levels of an Order Book 183 11.3 Consecutive Runs of a Rule 185 11.

4 Real-Time Signals and Alerts 186 Part Three Data Science Chapter 12 Basic Overview of Statistics 191 12.1 Histogram 191 12.2 First Moments 196 12.3 Hypothesis Testing 198 12.3.1 Normal p-values 198 12.3.2 Correlation 201 12.

3.2.1 Implementation 202 12.3.3 t-test: One Sample 202 12.3.3.1 Implementation 204 12.

3.4 t-test: Two Samples 204 12.3.4.1 Implementation 205 12.3.5 Sign Test 206 12.3.

5.1 Implementation of the Test 208 12.3.5.2 Median Test 211 12.3.6 Wilcoxon Signed-Rank Test 212 12.3.

7 Rank Correlation and Somers'' D 214 12.3.7.1 Implementation 216 12.3.8 Multiple Hypothesis Testing 221 12.3.8.

1 Bonferroni Correction 224 12.3.8.2 Sidák''s Correction 224 12.3.8.3 Holm''s Method 225 12.3.

8.4 Example 226 Chapter 13 Linear Regression 229 13.1 Linear Regression 230 13.2 Ordinary Least Squares 231 13.3 The Geometric Representation of Linear Regression 233 13.3.1 Moore-Penrose Pseudoinverse 235 13.3.

2 Adding Intercept 237 13.4 Implementation of the OLS 240 13.5 Significance of Parameters 243 13.6 How Good is the Fit: R2 244 13.6.1 Adjusted R-squared 247 13.7 Relationship with Maximum Likelihood Estimation and AIC with Small Sample Correction 248 13.8 Estimation Suite 252 13.

9 Comparing Two Nested Models: Towards a Stopping Rule 254 13.9.1 Comparing Two General Models 256 13.10 In-/Out-of-Sample Operations 257 13.11 Cross-validation 262 13.12 Conclusion 264 Chapter 14 Time Series Econometrics 265 14.1 Autoregressive and Moving Average Processes 265 14.1.

1 Introduction 265 14.1.2 AR(p) Process 266 14.1.2.1 Simulation 266 14.1.2.

2 Estimation of AR(p) Parameters 268 14.1.2.3 Least Square Method 268 14.1.2.4 Example 269 14.1.

2.5 Maximum Likelihood Estimator 269 14.1.2.6 Yule-Walker Technique 269 14.1.3 MA(q) Process 271 14.1.

3.1 Estimation of MA(q) Parameters 272 14.1.3.2 Simulation 272 14.1.3.3 Example 273 14.

1.4 ARMA(p, q) Process 273 14.1.4.1 Invertibility of the ARMA(p, q) Process 274 14.1.4.2 Hannan-Rissanen Algorithm: Two-Step Regression Estimation 274 14.

1.4.3 Yule-Walker Estimation 274 14.1.4.4 Maximum Likelihood Estimation 275 14.1.4.

5 Simulation 275 14.1.4.6 Forecast 276 14.1.5 ARIMA(p, d, q) Process 276 14.1.6 Code 276 14.

1.6.1 Simulation 277 14.1.6.2 Estimation 278 14.1.6.

3 Forecast 282 14.2 Stationarity and Granger Causality 285 14.2.1 Stationarity 285 14.2.2 Test of Stationarity - Dickey-Fuller and Augmented Dickey-Fuller Tests 286 14.2.3 Granger Causality 286 14.

3 Vector Autoregression 287 14.3.1 VAR(p) Process 288 14.3.1.1 Notation 288 14.3.1.

2 Estimator 288 14.3.1.3 Example 289 14.3.1.4 Code 293 14.3.

2 VARX(p, q) Process 297 14.3.2.1 Estimator 297 14.3.2.2 Code 298 Chapter 15 Fourier Transform 301 15.1 Complex Numbers 301 15.

1.1 Properties of Complex Numbers 302 15.2 Discrete Fourier Transform 308 15.3 Addendum: Quaternions 314 15.4 Addendum: Fractals 321 Chapter 16 Eigensystem and PCA 325 16.1 Theory 325 16.2 Algorithms 327 16.2.

1 QR Decomposition 328 16.2.2 QR Algorithm for Eigenvalues 330 16.2.3 Inverse Iteration 331 16.3 Implementation of Eigensystem Calculation 332 16.3.1 QR Decomposition 333 16.

3.2 Inverse Iteration 337 16.4 The Data Matrix and the Principal Component Analysis 341 16.4.1 The Data Matrix 341 16.4.2 PCA: The First Principal Component 344 16.4.

3 Second Principal Component 345 16.4.4 Terminology and Explained Variance 347 16.4.5 Dimensionality Reduction 349 16.4.6 PCA Regression (PCR) 350 16.5 Implementation of PCA 351 16.

6 Appendix: Determinant 354 16.6.1 Theory 354 16.6.2 Techniques to Calculate a Determinant 355 16.6.3 Implementation of the Determinant 356 Chapter 17 Outlier Detection 359 17.1 Local Outlier Factor 360 Chapter 18 Simulating Asset Prices 369 18.

1 Stochastic Volatility Process with Price Jumps 369 18.2 Towards the Numerical Example 371 18.2.1 Numerical Preliminaries 371 18.2.2 Implementing Stochastic Volatility Process with Jumps 374 18.3 Conclusion 378 Part Four Machine Learning Chapter 19 Basic Principles of Machine Learning 381 19.1 Non-Numeric Features and Normalisation 381 19.

1.1 Non-Numeric Features 381 19.1.1.1 Ordinal Features 382 19.1.1.2 Categorical Features 383 19.

1.2 Normalisation 383 19.1.2.1 Normal Score 384 19.1.2.2 Range Scaling 385 19.

2 Iteration: Constructing Machine Learning Algorithms 386 19.2.1 Iteration 386 19.2.2 Constructing Machine Learning Algorithms 389 Chapter 20 Linear Regression with Regularisation 391 20.1 Bias-Variance Trade-off 392 20.2 Regularisation 393 20.3 Ridge Regression 394 20.

4 Implementation of the Ridge Regression 396 20.4.1 Optimisation of the Regularisation Parameter 401 20.5 Lasso Regression 403 20.6 Implementation of the Lasso Regression 405 Chapter 21 Nearest Neighbours 419 21.1 k -Nearest Neighbours Classifier 419 21.2 Prototype Clustering 423 21.3 Feature Selection: Local Nearest Neighbours Approach.