12.5.2 Constrained Allocations 371

12.5.3 Parameter Selection 372

12.5.4 Long-Short Strategies 375

12.5.5 Backtesting 375 12.6 Common Features 381

12.6.1 Common Autocorrelation 385

12.6.2 Common Volatility 386

Chapter 13: Forecasting High-Frequency Data 389

13.1 High-Frequency Data 390

13.1.1 Data and Information Sources 390

13.1.2 Data Filters 391

13.1.3 Autocorrelation Properties 391

13.1.4 Parametric Models of High-Frequency Data 393

13.2 Neural Networks 395

13.2.1 Architecture 396

13.2.2 Data Processing 397

13.2.3 Backpropagation 398

13.2.4 Performance Measurement 399

13.2.5 Integration 400

13.3 Price Prediction Models Based on Chaotic Dynamics 401

13.3.1 Testing for Chaos 401

13.3.2 Nearest Neighbour Algorithms 403

13.3.3 Multivariate Embedding Methods 405

Technical Appendices 409

A.l Linear Regression* 409

A. 1.1 The Simple Linear Model 410

A. 1.2 Multivariate Models 412

A. 1.3 Properties of OLS Estimators 414

A. 1.4 Estimating the Covariance Matrix of the OLS Estimators 419

A.2 Statistical Inference 421

A.2.1 Hypothesis Testing and Confidence Intervals 421

A.2.2 /-tests 424

A.2.3 F-test 426

A.2.4 The Analysis of Variance 427

A.2.5 Wald, Lagrange Multiplier and Likelihood Ratio Tests 428

A.3 Residual Analysis 429

A.3.1 Autocorrelation 430

A.3.2 Unconditional Heteroscedasticity 432

A.3.3 Generalized Least Squares 433

A.4 Data Problems 436

A.4.1 Multicollinearity 436

A.4.2 Data Errors 437

A.4.3 Missing Data 439

A.4.4 Dummy Variables 440

A. 5 Prediction 443

A.5.1 Point Predictions and Confidence Intervals 443

A.5.2 Backtesting 444

A.5.3 Statistical and Operational Evaluation Methods 445

A.6 Maximum Likelihood Methods 447

A.6.1 The Likelihood Function, MLE and LR Tests 447

A.6.2 Properties of Maximum Likelihood Estimators 449

A.6.3 MLEs for a Normal Density Function 449

A.6.4 MLEs for Non-normal Density Functions 451

References 453

Tables 467

Index 475

Preface

This book is about the financial market models that are used by risk managers and investment analysts. It aims to provide a rigorous explanation of the theoretical ideas, but in practical and very clear terms. As concepts are introduced, real-world examples are provided in the text and, interactively, on the accompanying CD.

I have heard it said that too much academic research is focused on finding very precise answers to irrelevant questions. This book aims to provide academically acceptable answers to the questions that are really important for practitioners. It is written for a wide audience of practitioners, academics and students interested in the data analysis of financial asset prices.

It aims to help practitioners cut through the vast literature on financial market models, to focus on the most important and useful theoretical concepts. For academics the book highlights interesting research problems that are relevant to the day-to-day work of risk managers and investment analysts. For students, the comprehensive and self-contained nature of the text should appeal.

The book is divided into three parts:

Part I: Volatility and Correlation Analysis covers the estimation and forecasting of volatility and correlation for the pricing and hedging of options portfolios.

Part II: Modelling the Market Risk of Portfolios concerns factor modelling and the measurement of portfolio risk: the main focus is on modelling relationships between assets and/or risk factors using linear models.

Part III: Statistical Models for Financial Markets focuses on the time series analysis of financial markets.

A detailed summary of the content is provided in the introduction to each part. At the end of the book a low-level technical appendix is included; this covers the basic statistical theory that is necessary for the book to be self-contained.

Practitioners and academics share many important problems, and the communication between theory and practice is an essential part of model