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Format: 1 online resource (282 pages)

Edition: 1st ed.

ISBN: 9781107034723 , 9781107333567

Series Statement: Econometric Society Monographs v.Series Number 52

Content: This book presents a statistical theory for a class of nonlinear time-series models. It has particular relevance for the modeling of volatility in financial time series but the overall approach will be of interest to econometricians and statisticians in a variety of disciplines

Note: Intro -- Contents -- Preface -- Acronyms and Abbreviations -- 1 Introduction -- 1.1 Unobserved Components and Filters -- 1.2 Independence, White Noise and Martingale Differences -- 1.2.1 The Law of Iterated Expectations and Optimal Predictions -- 1.2.2 Definitions and Properties -- 1.3 Volatility -- 1.3.1 Stochastic Volatility -- 1.3.2 Generalized Autoregressive Conditional Heteroscedasticity -- 1.3.3 Exponential GARCH -- 1.3.4 Variance, Scale and Outliers -- 1.3.5 Location/Scale Models -- 1.4 Dynamic Conditional Score Models -- 1.5 Distributions and Quantiles -- 1.6 Plan of Book -- 2 Statistical Distributions and Asymptotic Theory -- 2.1 Distributions -- 2.1.1 Student's t Distribution -- 2.1.2 General Error Distribution -- 2.1.3 Beta Distribution -- 2.1.4 Gamma Distribution -- 2.2 Maximum Likelihood -- 2.2.1 Student's t Distribution -- 2.2.2 General Error Distribution -- 2.2.3 Gamma Distribution -- 2.2.4 Consistency and Asymptotic Normality* -- 2.3 Maximum Likelihood Estimation -- 2.3.1 An Information Matrix Lemma -- 2.3.2 Information Matrix for the First-Order Model -- 2.3.3 Information Matrix with the 0=x"010E Parameterization* -- 2.3.4 Asymptotic Distribution -- 2.3.5 Consistency and Asymptotic Normality* -- 2.3.6 Nonstationarity -- 2.3.7 Several Parameters -- 2.4 Higher Order Models -- 2.5 Tests -- 2.5.1 Serial Correlation -- 2.5.2 Goodness of Fit of Distributions -- 2.5.3 Residuals -- 2.5.4 Model Fit -- 2.6 Explanatory Variables -- 3 Location -- 3.1 Dynamic Student's t Location Model -- 3.2 Basic Properties -- 3.2.1 Generalization and Reduced Form -- 3.2.2 Moments of the Observations -- 3.2.3 Autocorrelation Function -- 3.3 Maximum Likelihood Estimation -- 3.3.1 Asymptotic Distribution of the Maximum Likelihood Estimator -- 3.3.2 Monte Carlo Experiments -- 3.3.3 Application to U.S. GDP -- 3.4 Parameter Restrictions* , 3.5 Higher Order Models and the State Space Form* -- 3.5.1 Linear Gaussian Models and the Kalman Filter -- 3.5.2 The DCS Model -- 3.5.3 QARMA Models -- 3.6 Trend and Seasonality -- 3.6.1 Local Level Model -- 3.6.2 Application to Weekly Hours of Employees in U.S. Manufacturing -- 3.6.3 Local Linear Trend -- 3.6.4 Stochastic Seasonal -- 3.6.5 Application to Rail Travel -- 3.6.6 QARIMA and Seasonal QARIMA Models* -- 3.7 Smoothing -- 3.7.1 Weights -- 3.7.2 Smoothing Recursions for Linear State Space Models -- 3.7.3 Smoothing Recursions for DCS Models -- 3.7.4 Conditional Mode Estimation and the Score -- 3.8 Forecasting -- 3.8.1 QARMA Models -- 3.8.2 State Space Form* -- 3.9 Components and Long Memory -- 3.10 General Error Distribution -- 3.11 Skew Distributions -- 3.11.1 How to Skew a Distribution -- 3.11.2 Dynamic Skew-t Location Model -- 4 Scale -- 4.1 Beta-tttt-EGARCH -- 4.2 Properties of Stationary Beta-tttt-EGARCH Models -- 4.2.1 Exponential GARCH -- 4.2.2 Moments -- 4.2.3 Autocorrelation Functions of Squares and Powersof Absolute Values -- 4.2.4 Autocorrelations and Kurtosis -- 4.3 Leverage Effects -- 4.4 Gamma-GED-EGARCH -- 4.5 Forecasting -- 4.5.1 Beta-t-EGARCH -- 4.5.2 Gamma-GED-EGARCH -- 4.5.3 Integrated Exponential Models -- 4.5.4 Predictive Distribution -- 4.6 Maximum Likelihood Estimation and Inference -- 4.6.1 Asymptotic Theory for Beta-t-EGARCH -- 4.6.2 Monte Carlo Experiments -- 4.6.3 Gamma-GED-EGARCH -- 4.6.4 Leverage -- 4.7 Beta-tttt-GARCH -- 4.7.1 Properties of First-Order Model -- 4.7.2 Leverage Effects -- 4.7.3 Link with Beta-t-EGARCH -- 4.7.4 Estimation and Inference -- 4.7.5 Gamma-GED-GARCH -- 4.8 Smoothing -- 4.9 Application to Hang Seng and Dow Jones -- 4.10 Two Component Models -- 4.11 Trends, Seasonals and Explanatory Variables in Volatility Equations -- 4.12 Changing Location -- 4.12.1 Explanatory Variables , 4.12.2 Stochastic Location and Stochastic Scale -- 4.13 Testing for Changing Volatility and Leverage -- 4.13.1 Portmanteau Test for Changing Volatility -- 4.13.2 Martingale Difference Test -- 4.13.3 Leverage -- 4.13.4 Diagnostics -- 4.14 Skew Distributions -- 4.15 Time-Varying Skewness and Kurtosis* -- 5 Location/Scale Models for Non-negative Variables -- 5.1 General Properties -- 5.1.1 Heavy Tails -- 5.1.2 Moments and Autocorrelations -- 5.1.3 Forecasts -- 5.1.4 Asymptotic Distribution of Maximum Likelihood Estimators -- 5.2 Generalized Gamma Distribution -- 5.2.1 Moments -- 5.2.2 Forecasts -- 5.2.3 Maximum Likelihood Estimation -- 5.3 Generalized Beta Distribution -- 5.3.1 Log-Logistic Distribution -- 5.3.2 Moments, Autocorrelations and Forecasts -- 5.3.3 Maximum Likelihood Estimation -- 5.3.4 Burr Distribution -- 5.3.5 Generalized Pareto Distribution -- 5.3.6 F Distribution -- 5.4 Log-Normal Distribution -- 5.5 Monte Carlo Experiments -- 5.6 Leverage, Long Memory and Diurnal Variation -- 5.7 Tests and Model Selection -- 5.8 Estimating Volatility from the Range -- 5.8.1 Application to Paris CAC and Dow Jones -- 5.8.2 The Range-EGARCH Model -- 5.9 Duration -- 5.10 Realized Volatility -- 5.11 Count Data and Qualitative Observations -- 6 Dynamic Kernel Density Estimation and Time-Varying Quantiles -- 6.1 Kernel Density Estimation for Time Series -- 6.1.1 Filtering and Smoothing -- 6.1.2 Estimation -- 6.1.3 Correcting for Changing Mean and Variance -- 6.1.4 Specification and Diagnostic Checking -- 6.2 Time-Varying Quantiles -- 6.2.1 Kernel-Based Estimation -- 6.2.2 Direct Estimation of Individual Quantiles -- 6.3 Forecasts -- 6.4 Application to NASDAQ Returns -- 6.4.1 Direct Modelling of Returns -- 6.4.2 ARMA-GARCH Residuals -- 6.4.3 Bandwidth and Tails -- 7 Multivariate Models, Correlation and Association -- 7.1 Multivariate Distributions , 7.1.1 Estimation -- 7.1.2 Regression -- 7.1.3 Dynamic Models -- 7.2 Multivariate Location Models -- 7.2.1 Structural Time Series Models -- 7.2.2 DCS Model for the Multivariate t -- 7.2.3 Asymptotic Theory* -- 7.2.4 Regression and Errors in Variables -- 7.3 Dynamic Correlation -- 7.3.1 A Bivariate Gaussian Model -- 7.3.2 Time-Varying Parameters in Regression -- 7.3.3 Multivariate t Distribution -- 7.3.4 Tests of Changing Correlation -- 7.4 Dynamic Multivariate Scale -- 7.5 Dynamic Scale and Association -- 7.6 Copulas -- 7.6.1 Copulas and Quantiles -- 7.6.2 Measures of Association -- 7.6.3 Maximum Likelihood Estimation -- 7.6.4 Dynamic Copulas -- 7.6.5 Tests against Changing Association -- 8 Conclusions and Further Directions -- Appendix A: Appendix A: Derivation of Formulae in the Information Matrix -- A.1 Unconditional mean parameterization -- A.2 Paramerization with 0=x"010E -- A.3 Leverage -- Appendix B: Appendix B: Autocorrelation Functions -- B.1 Beta-t-EGARCH -- B.2 Gamma-GED-EGARCH -- B.3 Beta-t-GARCH -- Appendix C: Appendix C: GED Information Matrix -- Appendix D: Appendix D: The Order of GARCH Models -- Appendix E: Appendix E: Computer Programs -- Bibliography -- Author Index -- Subject Index

Additional Edition: Print version Harvey, Andrew C. Dynamic Models for Volatility and Heavy Tails New York : Cambridge University Press,c2013 ISBN 9781107034723

Language: English

Keywords: Electronic books

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