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The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.
Mathematical statistics --- AA / International- internationaal --- 305.970 --- Algemeenheden: Autoregression and moving average representation. ARIMA. ARMAX. Lagrange multiplier. Wald. Function (mis) specification. Autocorrelation. Homoscedasticity. Heteroscedasticity. ARCH. GARCH. Integration and co-integration. Unit roots. --- Econometrics --- Finance --- Time-series analysis --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Probabilities --- Economics, Mathematical --- Statistics --- Mathematical models --- Algemeenheden: Autoregression and moving average representation. ARIMA. ARMAX. Lagrange multiplier. Wald. Function (mis) specification. Autocorrelation. Homoscedasticity. Heteroscedasticity. ARCH. GARCH. Integration and co-integration. Unit roots --- Finance - Mathematical models --- Business, Economy and Management --- Economics --- Econometrics. --- Time-series analysis. --- Mathematical models.
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In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.
Time-series analysis --- Mathematical statistics --- Kalman filtering --- Kalman, filtrage de --- Série chronologique --- Time-series analysis. --- Kalman filtering. --- Filtering, Kalman --- Analysis of time series --- Control theory --- Estimation theory --- Prediction theory --- Stochastic processes --- Autocorrelation (Statistics) --- Harmonic analysis --- Probabilities --- 304.5 --- 305.974 --- AA / International- internationaal --- Techniek van de statistische-econometrische voorspellingen. Prognose in de econometrie --- Time varying coefficients. Kalman Filter --- Séries chronologiques --- Economic forecasting --- Prévision économique --- Time series analysis
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The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.
Econometrics. --- Finance --- Time-series analysis. --- Mathematical models. --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities --- Economics, Mathematical --- Statistics --- Business, Economy and Management --- Economics
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This 2004 volume offers a broad overview of developments in the theory and applications of state space modeling. With fourteen chapters from twenty-three contributors, it offers a unique synthesis of state space methods and unobserved component models that are important in a wide range of subjects, including economics, finance, environmental science, medicine and engineering. The book is divided into four sections: introductory papers, testing, Bayesian inference and the bootstrap, and applications. It will give those unfamiliar with state space models a flavour of the work being carried out as well as providing experts with valuable state of the art summaries of different topics. Offering a useful reference for all, this accessible volume makes a significant contribution to the literature of this discipline.
State-space methods --- System analysis --- Congresses --- AA / International- internationaal --- 304.5 --- 303.5 --- 305.974 --- -System analysis --- -003 --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Techniek van de statistische-econometrische voorspellingen. Prognose in de econometrie. --- Theorie van correlatie en regressie. (OLS, adjusted LS, weighted LS, restricted LS, GLS, SLS, LIML, FIML, maximum likelihood). Parametric and non-parametric methods and theory (wiskundige statistiek). --- Time varying coefficients. Kalman Filter. --- Conferences - Meetings --- 003 --- Theorie van correlatie en regressie. (OLS, adjusted LS, weighted LS, restricted LS, GLS, SLS, LIML, FIML, maximum likelihood). Parametric and non-parametric methods and theory (wiskundige statistiek) --- Techniek van de statistische-econometrische voorspellingen. Prognose in de econometrie --- Time varying coefficients. Kalman Filter --- Business, Economy and Management --- Economics --- State-space methods - Congresses --- System analysis - Congresses --- Quantitative methods (economics) --- econometrie
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