Luc Bauwens, PhD, is Professor of Economics at the Université catholique de Louvain (Belgium), where he is also President of the Center for Operations Research and Econometrics (CORE). He has written more than 100 published papers on the topics of econometrics, statistics, and microeconomics.Christian Hafner, PhD, is Professor and President of the Louvain School of Statistics, Biostatistics, and Actuarial Science (LSBA) at the Université catholique de Louvain (Belgium). He has published extensively in the areas of time series econometrics, applied nonparametric statistics, and empirical finance.Sebastien Laurent, PhD, is Associate Professor of Econometrics in the Department of Quantitative Economics at Maastricht University (The Netherlands). Dr. Laurent's current areas of research interest include financial econometrics and computational econometrics.

"Conceived and written by over two-dozen experts in the fi eld, the book cohesively demonstrates how 'volatile' certain statistical decision-making techniques can be when solving a range of financial problems." (Zentralblatt MATH 2016)

• 1. Volatility Models 1 1.1 Introduction 11.2 GARCH 11.3 Stochastic Volatility 311.4 Realized Volatility 42Part I. ARCH and SV2. Nonlinear ARCH Models 632.1 Introduction 632.2 Standard GARCH model 642.3 Predecessors to Nonlinear GARCH 652.4 Nonlinear ARCH and GARCH 672.5 Testing 762.6 Estimation 812.7 Forecasting 832.8 Multiplicative Decomposition 862.9 Conclusion 883. Mixture and Regime-switching GARCH Models 893.1 Introduction 893.2 Regime-switching GARCH models 923.3 Stationarity and Moment Structure 1023.4 Regime Inference, Likelihood Functions, and Volatility Forecasting 1113.5 Application of Mixture GARCH Models 1193.6 Conclusion 1244. Forecasting High Dimensional Covariance Matrices 1294.1 Introduction 1294.2 Notation 1304.3 Rolling-Window Forecasts 1314.4 Dynamic Models 1364.5 High-Frequency Based Forecasts 1474.6 Forecast Evaluation 1544.7 Conclusion 1575. Mean, Volatility and Skewness Spillovers in Equity Markets 1595.1 Introduction 1595.2 Data and Summary Statistics 1625.3 Empirical Results 1715.4 Conclusion 1776. Relating Stochastic Volatility Estimation Methods 1856.1 Introduction 1856.2 Theory and Methodology 1886.3 Comparison of Methods 2016.4 Estimating Volatility Models in Practice 2096.5 Conclusion 2177. Multivariate Stochastic Volatility Models 2217.1 Introduction 2217.2 MSV model 2237.3 Factor MSV model 2317.4 Applications to Stock Indices Returns 2377.5 Conclusion 2448. Model Selection and Testing of Volatility Models 2498.1 Introduction 2498.2 Model Selection and Testing 2528.3 Empirical Example 2658.4 Conclusion 277Part II. Other models and methods9. Multiplicative Error Models 2819.1 Introduction 2819.2 Theory and Methodology 2839.3 MEM Application 2939.4 MEM Extensions 3029.5 Conclusion 30810. Locally Stationary Volatility Modeling 31110.1 Introduction 31110.2 Empirical evidences 31410.3 Locally Stationary Processes 31910.4 Locally Stationary Volatility Models 32310.5 Multivariate Models for Locally Stationary Volatility 33110.6 Conclusion 33311. Nonparametric and Semiparametric Volatility Models 33511.1 Introduction 33511.2 Nonparametric and Semiparametric Univariate Models 33811.3 Nonparametric and Semiparametric Multivariate Volatility Models 35411.4 Empirical Analysis 36011.5 Conclusion 36312. Copula-based Volatility Models 36712.1 Introduction 36712.2 Definition and Properties of Copulas 36912.3 Estimation 37512.4 Dynamic Copulas 38112.5 Value-at-Risk 38712.6 Multivariate Static copulas 38912.7 Conclusion 395Part III. Realized Volatility13. Realized Volatility: Theory and Applications 39913.1 Introduction 39913.2 Modelling Framework 40013.3 Issues in Handling Intra-day Transaction Databases 40413.4 Realized Variance and Covariance 41114.5 Modelling and Forecasting 42213.6 Asset Pricing 42613.7 Estimating Continuous Time Models 43114. Likelihood-Based Volatility Estimators 43514.1 Introduction 43514.2 Volatility Estimation 43814.3 Covariance Estimation 44714.4 Empirical Application 45014.5 Conclusion 45215. HAR Modeling for Realized Volatility Forecasting 45315.1 Introduction 45315.2 Stylized Facts 45515.3 Heterogeneity and Volatility Persistence 45715.4 HAR Extensions 46315.5 Multivariate Models 46915.6 Applications 47315.7 Conclusion 47816. Forecasting volatility with MIDAS 48116.1 Introduction 48116.2 MIDAS Regression Models and Volatility Forecasting 48216.3 Likelihood-based Methods 49216.4 Multivariate Models 50516.5 Conclusion 50717. Jumps 50917.1 Introduction 50917.2 Estimators of Integrated Variance and Integrated Covariance 51917.3 Testing for the Presence of Jumps 54817.4 Conclusion 56318. Jumps, Periodicity and Microstructure Noise 56518.1 Introduction 56518.2 Model 56818.3 Price Jump Detection Method 57018.4 Simulation Study 57618.5 Comparison on NYSE-Stock Prices 58118.6 Conclusion 58319. Volatility Forecasts Evaluation and Comparison 58519.1 Introduction 58519.2 Notation 58819.3 Single Forecast Evaluation 59019.4 Loss Functions and the Latent Variable Problem 59319.5 Pairwise Comparison 59719.6 Multiple Comparison 60119.7 Consistency of the Ordering and Inference on Forecast Performances 60719.8 Conclusion 613Index 615Bibliography 629

Luc Bauwens, PhD, is Professor of Economics at the Université catholique de Louvain (Belgium), where he is also President of the Center for Operations Research and Econometrics (CORE). He has written more than 100 published papers on the topics of econometrics, statistics, and microeconomics.Christian Hafner, PhD, is Professor and President of the Louvain School of Statistics, Biostatistics, and Actuarial Science (LSBA) at the Université catholique de Louvain (Belgium). He has published extensively in the areas of time series econometrics, applied nonparametric statistics, and empirical finance.Sebastien Laurent, PhD, is Associate Professor of Econometrics in the Department of Quantitative Economics at Maastricht University (The Netherlands). Dr. Laurent's current areas of research interest include financial econometrics and computational econometrics.

"Conceived and written by over two-dozen experts in the fi eld, the book cohesively demonstrates how 'volatile' certain statistical decision-making techniques can be when solving a range of financial problems." (Zentralblatt MATH 2016)

• 1. Volatility Models 1 1.1 Introduction 11.2 GARCH 11.3 Stochastic Volatility 311.4 Realized Volatility 42Part I. ARCH and SV2. Nonlinear ARCH Models 632.1 Introduction 632.2 Standard GARCH model 642.3 Predecessors to Nonlinear GARCH 652.4 Nonlinear ARCH and GARCH 672.5 Testing 762.6 Estimation 812.7 Forecasting 832.8 Multiplicative Decomposition 862.9 Conclusion 883. Mixture and Regime-switching GARCH Models 893.1 Introduction 893.2 Regime-switching GARCH models 923.3 Stationarity and Moment Structure 1023.4 Regime Inference, Likelihood Functions, and Volatility Forecasting 1113.5 Application of Mixture GARCH Models 1193.6 Conclusion 1244. Forecasting High Dimensional Covariance Matrices 1294.1 Introduction 1294.2 Notation 1304.3 Rolling-Window Forecasts 1314.4 Dynamic Models 1364.5 High-Frequency Based Forecasts 1474.6 Forecast Evaluation 1544.7 Conclusion 1575. Mean, Volatility and Skewness Spillovers in Equity Markets 1595.1 Introduction 1595.2 Data and Summary Statistics 1625.3 Empirical Results 1715.4 Conclusion 1776. Relating Stochastic Volatility Estimation Methods 1856.1 Introduction 1856.2 Theory and Methodology 1886.3 Comparison of Methods 2016.4 Estimating Volatility Models in Practice 2096.5 Conclusion 2177. Multivariate Stochastic Volatility Models 2217.1 Introduction 2217.2 MSV model 2237.3 Factor MSV model 2317.4 Applications to Stock Indices Returns 2377.5 Conclusion 2448. Model Selection and Testing of Volatility Models 2498.1 Introduction 2498.2 Model Selection and Testing 2528.3 Empirical Example 2658.4 Conclusion 277Part II. Other models and methods9. Multiplicative Error Models 2819.1 Introduction 2819.2 Theory and Methodology 2839.3 MEM Application 2939.4 MEM Extensions 3029.5 Conclusion 30810. Locally Stationary Volatility Modeling 31110.1 Introduction 31110.2 Empirical evidences 31410.3 Locally Stationary Processes 31910.4 Locally Stationary Volatility Models 32310.5 Multivariate Models for Locally Stationary Volatility 33110.6 Conclusion 33311. Nonparametric and Semiparametric Volatility Models 33511.1 Introduction 33511.2 Nonparametric and Semiparametric Univariate Models 33811.3 Nonparametric and Semiparametric Multivariate Volatility Models 35411.4 Empirical Analysis 36011.5 Conclusion 36312. Copula-based Volatility Models 36712.1 Introduction 36712.2 Definition and Properties of Copulas 36912.3 Estimation 37512.4 Dynamic Copulas 38112.5 Value-at-Risk 38712.6 Multivariate Static copulas 38912.7 Conclusion 395Part III. Realized Volatility13. Realized Volatility: Theory and Applications 39913.1 Introduction 39913.2 Modelling Framework 40013.3 Issues in Handling Intra-day Transaction Databases 40413.4 Realized Variance and Covariance 41114.5 Modelling and Forecasting 42213.6 Asset Pricing 42613.7 Estimating Continuous Time Models 43114. Likelihood-Based Volatility Estimators 43514.1 Introduction 43514.2 Volatility Estimation 43814.3 Covariance Estimation 44714.4 Empirical Application 45014.5 Conclusion 45215. HAR Modeling for Realized Volatility Forecasting 45315.1 Introduction 45315.2 Stylized Facts 45515.3 Heterogeneity and Volatility Persistence 45715.4 HAR Extensions 46315.5 Multivariate Models 46915.6 Applications 47315.7 Conclusion 47816. Forecasting volatility with MIDAS 48116.1 Introduction 48116.2 MIDAS Regression Models and Volatility Forecasting 48216.3 Likelihood-based Methods 49216.4 Multivariate Models 50516.5 Conclusion 50717. Jumps 50917.1 Introduction 50917.2 Estimators of Integrated Variance and Integrated Covariance 51917.3 Testing for the Presence of Jumps 54817.4 Conclusion 56318. Jumps, Periodicity and Microstructure Noise 56518.1 Introduction 56518.2 Model 56818.3 Price Jump Detection Method 57018.4 Simulation Study 57618.5 Comparison on NYSE-Stock Prices 58118.6 Conclusion 58319. Volatility Forecasts Evaluation and Comparison 58519.1 Introduction 58519.2 Notation 58819.3 Single Forecast Evaluation 59019.4 Loss Functions and the Latent Variable Problem 59319.5 Pairwise Comparison 59719.6 Multiple Comparison 60119.7 Consistency of the Ordering and Inference on Forecast Performances 60719.8 Conclusion 613Index 615Bibliography 629