Generalized Autoregressive Conditional Heteroscedastic Time Series Models PDF Download
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Author: Michael S. Lo
Publisher:
ISBN:
Category : Heteroscedasticity
Languages : en
Pages : 0
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Book Description
Author: Michael S. Lo
Publisher:
ISBN:
Category : Heteroscedasticity
Languages : en
Pages : 0
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Book Description
Author: Daniel Straumann
Publisher: Springer Science & Business Media
ISBN: 3540269789
Category : Business & Economics
Languages : en
Pages : 239
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Book Description
In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.
Author: Yao Zheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
The estimation for time series models with heavy-tailed innovations has been widely discussed in the literature, while the corresponding goodness-of-fit tests have attracted less attention. This is mainly because the commonly used autocorrelation function in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. In the light of the fact that a bounded random variable has finite moments of all orders, we address this problem by first transforming the residuals with a bounded and increasing function. Specifically, this paper considers the autocorrelation function of the transformed absolute residuals from a fitted GARCH model. With the corresponding residual empirical distribution function naturally employed as the transformation, a robust goodness-of-fit test is constructed. The asymptotic null distribution of the test statistic is derived, and simulation experiments are conducted to assess its finite-sample performance. A real data example is analyzed to further illustrate its usefulness.
Author: Tim Bollerslev
Publisher:
ISBN:
Category : Economics
Languages : en
Pages : 280
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Author: B. Noriega
Publisher: Independently Published
ISBN: 9781798663752
Category : Mathematics
Languages : en
Pages : 150
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Book Description
Conditional variance models are appropriate for time series that do not exhibit significant autocorrelation, but are serially dependent. For modeling time series that are both autocorrelated and serially dependent, you can consider using a composite conditional mean and variance model.Two characteristics of financial time series that conditional variance models address are: -Volatility clustering. Volatility is the conditional standard deviation of a time series. Autocorrelation in the conditional variance process results in volatility clustering. The GARCH model and its variants model autoregression in the variance series.-Leverage effects. The volatility of some time series responds more to large decreases than to large increases. This asymmetric clustering behavior is known as the leverage effect. The EGARCH and GJR models have leverage terms to model this asymmetry.The generalized autoregressive conditional heteroscedastic (GARCH) model is an extension of Engle's ARCH model for variance heteroscedasticity. If a series exhibits volatility clustering, this suggests that past variances might be predictive of the current variance. The GARCH(P, Q) model is an autoregressive moving average model for conditional variances, with P GARCH coefficients associated with lagged variances, and Q ARCH coefficients associated with lagged squared innovations.The exponential GARCH (EGARCH) model is a GARCH variant that models the logarithm of the conditional variance process. In addition to modeling the logarithm, the EGARCH model has additional leverage terms to capture asymmetry in volatility clustering. The EGARCH(P, Q) model has P GARCH coefficients associated with lagged log variance terms, Q ARCH coefficients associated with the magnitude of lagged standardized innovations, and Q leverage coefficients associated with signed, lagged standardized innovations.
Author: Indeewara Perera
Publisher:
ISBN:
Category :
Languages : en
Pages : 56
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Book Description
Specification tests are developed for the conditional distribution of a dependent process {Xi} in a family of nonlinear time-series models. The family includes several Generalized AutoRegressive Conditional Heteroscedastic [GARCH] models that are widely used in finance and economics. Such tests are essential for ensuring the validity of density forecasts that are based on the assumed model. The tests are implemented using a bootstrap procedure, because the test statistics are not asymptotically pivotal. A novel method is developed for verifying the validity of the bootstrap tests for a given model; this involves simultaneously embedding the process under the null hypothesis and the bootstrap process in a system of stochastic recurrence equations. The method is illustrated for a well-known GARCH model. Within the specification testing literature, a feature that distinguishes this paper is that the conditional distribution of Xi under the null model, depends on the unobservable past values {. . . , X-2, X-1} extending back to the infinite past. The theory for testing the specification of the conditional distribution of Xi in such parametric models has not been developed in the general setting considered in this paper. The tests performed well in a simulation study, and a data example illustrates the tests.
Author: Perez M.
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534845459
Category :
Languages : en
Pages : 204
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Book Description
Econometrics Toolbox(TM) provides functions for modeling economic data. You can select and calibrate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate ARMAX/GARCH composite models with several GARCH variants, multivariate VARMAX models, and cointegration analysis. This book focuses on conditional variance models. Conditional variance models attempt to address volatility clustering in univariate time series models to improve parameter estimates and forecast accuracy. To model volatility, Econometrics Toolbox(TM) supports the standard generalized autoregressive conditional heteroscedastic (ARCH/GARCH) model, the exponential GARCH (EGARCH) model, and the Glosten, Jagannathan, and Runkle (GJR) model.
Author: Ratnayake Mudiyanselage Isuru Panduka Ratnayake
Publisher:
ISBN:
Category :
Languages : en
Pages : 197
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Book Description
"Models with a conditional heteroscedastic variance structure play a vital role in many applications, including modeling financial volatility. In this dissertation several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroscedastic model, are further generalized to provide more effective modeling of price range data well as count data. First, the Conditional Autoregressive Range (CARR) model is generalized by introducing a composite range-based multiplicative component formulation named the Composite CARR model. This formulation enables a more effective modeling of the long and short-term volatility components present in price range data. It treats the long-term volatility as a stochastic component that in itself exhibits conditional volatility. The Generalized Feedback Asymmetric CARR model presented in this dissertation is a generalization of the Feedback Asymmetric CARR model, with lagged cross-conditional range terms added to allow complete feedback across the two equations that model upward and downward price ranges. A regime-switching Threshold Asymmetric CARR model is also proposed. Its formulation captures both asymmetry and non-linearity, which are two main characteristics that exist in the price range data. This model handles asymmetry and non-linearity better than its range-based competitors, based on the Akaike's Information Criteria. In addition to the above models, a Time Varying Zero Inflated Poisson Integer GARCH model is introduced. This model enables the modeling of time series of count data with excess number of zeroes where this excess varies with time. In this model, the zero inflation component is modeled either as a deterministic function of time or as a vector of stochastic variables"--Abstract, page iv.
Author: Anil K. Bera
Publisher: London : Department of Economics, University of Western Ontario
ISBN:
Category : Time-series analysis
Languages : en
Pages : 42
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Book Description
Author: Ruey S. Tsay
Publisher: John Wiley & Sons
ISBN: 1119264073
Category : Mathematics
Languages : en
Pages : 512
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Book Description
A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors—noted experts in the field—explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models. The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational methods. Parametric and nonparametric methods and nonlinear and non-Gaussian state space models provide a much wider range of tools for time series analysis. In addition, advances in computing and data collection have made available large data sets and high-frequency data. These new data make it not only feasible, but also necessary to take into consideration the nonlinearity embedded in most real-world time series. This vital guide: • Offers research developed by leading scholars of time series analysis • Presents R commands making it possible to reproduce all the analyses included in the text • Contains real-world examples throughout the book • Recommends exercises to test understanding of material presented • Includes an instructor solutions manual and companion website Written for students, researchers, and practitioners who are interested in exploring nonlinearity in time series, Nonlinear Time Series Analysis offers a comprehensive text that explores the advantages and limitations of the nonlinear models and methods and demonstrates the improvements upon linear time series models.
