Hybrid Quantile Regression Estimation For Time Series Models With Conditional Heteroscedasticity

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Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity

Author : Yao Zheng
Publisher :
ISBN 13 :
Total Pages : 53 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity by : Yao Zheng

Download or read book Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity written by Yao Zheng and published by . This book was released on 2016 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of conditional heteroscedastic models, the generalized autoregressive conditional heteroscedastic (GARCH) process is the most popular and influential one. So far, feasible quantile regression methods for this task have been confined to a variant of the GARCH model, the linear GARCH model, owing to its tractable conditional quantile structure. This paper considers the widely used GARCH model. An easy-to-implement hybrid conditional quantile estimation procedure is developed based on a simple albeit nontrivial transformation. Asymptotic properties of the proposed estimator and statistics are derived, which facilitate corresponding inferences. To approximate the asymptotic distribution of the quantile regression estimator, we introduce a mixed bootstrapping procedure, where a time-consuming optimization is replaced by a sample averaging. Moreover, diagnostic tools based on the residual quantile autocorrelation function are constructed to check the adequacy of the fitted conditional quantiles. Simulation experiments are carried out to assess the finite-sample performance of the proposed approach. The favorable performance of the conditional quantile estimator and the usefulness of the inference tools are further illustrated by an empirical application.

Quantile Regression

Author : Marilena Furno
Publisher : John Wiley & Sons
ISBN 13 : 111886364X
Total Pages : 311 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Quantile Regression by : Marilena Furno

Download or read book Quantile Regression written by Marilena Furno and published by John Wiley & Sons. This book was released on 2018-07-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Quantile Regression

Author : Marilena Furno
Publisher : John Wiley & Sons
ISBN 13 : 1118863593
Total Pages : 307 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Quantile Regression by : Marilena Furno

Download or read book Quantile Regression written by Marilena Furno and published by John Wiley & Sons. This book was released on 2018-09-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Quantile Regression

Author : Marilena Furno
Publisher : Wiley
ISBN 13 : 9781118863596
Total Pages : 0 pages
Book Rating : 4.8/5 (635 download)

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Book Synopsis Quantile Regression by : Marilena Furno

Download or read book Quantile Regression written by Marilena Furno and published by Wiley. This book was released on 2018-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Quantile Regression for Cross-Sectional and Time Series Data

Author : Jorge M. Uribe
Publisher : Springer Nature
ISBN 13 : 3030445046
Total Pages : 63 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Quantile Regression for Cross-Sectional and Time Series Data by : Jorge M. Uribe

Download or read book Quantile Regression for Cross-Sectional and Time Series Data written by Jorge M. Uribe and published by Springer Nature. This book was released on 2020-03-30 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief addresses the estimation of quantile regression models from a practical perspective, which will support researchers who need to use conditional quantile regression to measure economic relationships among a set of variables. It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature. All applications are illustrated with R.

Handbook of Quantile Regression

Author : Roger Koenker
Publisher : CRC Press
ISBN 13 : 1498725295
Total Pages : 463 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Quantile Regression by : Roger Koenker

Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

Quantile Regression

Author : I. Gusti Ngurah Agung
Publisher : John Wiley & Sons
ISBN 13 : 1119715180
Total Pages : 496 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Quantile Regression by : I. Gusti Ngurah Agung

Download or read book Quantile Regression written by I. Gusti Ngurah Agung and published by John Wiley & Sons. This book was released on 2021-06-18 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: QUANTILE REGRESSION A thorough presentation of Quantile Regression designed to help readers obtain richer information from data analyses The conditional least-square or mean-regression (MR) analysis is the quantitative research method used to model and analyze the relationships between a dependent variable and one or more independent variables, where each equation estimation of a regression can give only a single regression function or fitted values variable. As an advanced mean regression analysis, each estimation equation of the mean-regression can be used directly to estimate the conditional quantile regression (QR), which can quickly present the statistical results of a set nine QR(τ)s for τ(tau)s from 0.1 up to 0.9 to predict detail distribution of the response or criterion variable. QR is an important analytical tool in many disciplines such as statistics, econometrics, ecology, healthcare, and engineering. Quantile Regression: Applications on Experimental and Cross Section Data Using EViews provides examples of statistical results of various QR analyses based on experimental and cross section data of a variety of regression models. The author covers the applications of one-way, two-way, and n-way ANOVA quantile regressions, QRs with multi numerical predictors, heterogeneous QRs, and latent variables QRs, amongst others. Throughout the text, readers learn how to develop the best possible quantile regressions and how to conduct more advanced analysis using methods such as the quantile process, the Wald test, the redundant variables test, residual analysis, the stability test, and the omitted variables test. This rigorous volume: Describes how QR can provide a more detailed picture of the relationships between independent variables and the quantiles of the criterion variable, by using the least-square regression Presents the applications of the test for any quantile of any numerical response or criterion variable Explores relationship of QR with heterogeneity: how an independent variable affects a dependent variable Offers expert guidance on forecasting and how to draw the best conclusions from the results obtained Provides a step-by-step estimation method and guide to enable readers to conduct QR analysis using their own data sets Includes a detailed comparison of conditional QR and conditional mean regression Quantile Regression: Applications on Experimental and Cross Section Data Using EViews is a highly useful resource for students and lecturers in statistics, data analysis, econometrics, engineering, ecology, and healthcare, particularly those specializing in regression and quantitative data analysis.

Handbook of Quantile Regression

Author : Roger Koenker
Publisher : CRC Press
ISBN 13 : 1351646567
Total Pages : 739 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Handbook of Quantile Regression by : Roger Koenker

Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

Quantile Regression

Author : Cristina Davino
Publisher : John Wiley & Sons
ISBN 13 : 1118752716
Total Pages : 288 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Quantile Regression by : Cristina Davino

Download or read book Quantile Regression written by Cristina Davino and published by John Wiley & Sons. This book was released on 2013-10-24 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.

Quantile Regression

Author : Lingxin Hao
Publisher : SAGE Publications
ISBN 13 : 1483316904
Total Pages : 142 pages
Book Rating : 4.4/5 (833 download)

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Book Synopsis Quantile Regression by : Lingxin Hao

Download or read book Quantile Regression written by Lingxin Hao and published by SAGE Publications. This book was released on 2007-04-18 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile Regression, the first book of Hao and Naiman′s two-book series, establishes the seldom recognized link between inequality studies and quantile regression models. Though separate methodological literature exists for each subject, the authors seek to explore the natural connections between this increasingly sought-after tool and research topics in the social sciences. Quantile regression as a method does not rely on assumptions as restrictive as those for the classical linear regression; though more traditional models such as least squares linear regression are more widely utilized, Hao and Naiman show, in their application of quantile regression to empirical research, how this model yields a more complete understanding of inequality. Inequality is a perennial concern in the social sciences, and recently there has been much research in health inequality as well. Major software packages have also gradually implemented quantile regression. Quantile Regression will be of interest not only to the traditional social science market but other markets such as the health and public health related disciplines. Key Features: Establishes a natural link between quantile regression and inequality studies in the social sciences Contains clearly defined terms, simplified empirical equations, illustrative graphs, empirical tables and graphs from examples Includes computational codes using statistical software popular among social scientists Oriented to empirical research

Investigations on Quantile Regression

Author : Jau-Er Chen
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783843385299
Total Pages : 108 pages
Book Rating : 4.3/5 (852 download)

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Book Synopsis Investigations on Quantile Regression by : Jau-Er Chen

Download or read book Investigations on Quantile Regression written by Jau-Er Chen and published by LAP Lambert Academic Publishing. This book was released on 2010-12 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression, as introduced in Koenker and Bassett (1978), is gradually emerging as a comprehensive approach to the econometric analysis. Quantile regression estimation has not only the robustness advantages of semiparametric models which involve the distribution-free assumption but also the information extraction over whole conditional distribution. The goals of this monograph are aimed at clarifying the theoretical parts and facilitating the practical implementation of quantile regression methods. Typically, the emphasis is put on implementing quantile regression in time series models. This is because that the performance of the tests constructed for quantile regression estimators in time series has not been well explored. A comprehensive study on estimating the covariance matrix of quantile regression estimators are presented in this monograph. We also implements the quantile regression method to analyze the VaR of Nikkei 225 stock index. In short, estimation, asymptotic normality, statistical inferences and applications on quantile regression methods constitute the framework of this monograph.

Quantile Regression

Author : Roger Koenker
Publisher : Cambridge University Press
ISBN 13 : 1139444719
Total Pages : 367 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Quantile Regression by : Roger Koenker

Download or read book Quantile Regression written by Roger Koenker and published by Cambridge University Press. This book was released on 2005-05-05 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Quantile Regression for Spatial Data

Author : Daniel P. McMillen
Publisher : Springer Science & Business Media
ISBN 13 : 3642318150
Total Pages : 69 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Quantile Regression for Spatial Data by : Daniel P. McMillen

Download or read book Quantile Regression for Spatial Data written by Daniel P. McMillen and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression analysis differs from more conventional regression models in its emphasis on distributions. Whereas standard regression procedures show how the expected value of the dependent variable responds to a change in an explanatory variable, quantile regressions imply predicted changes for the entire distribution of the dependent variable. Despite its advantages, quantile regression is still not commonly used in the analysis of spatial data. The objective of this book is to make quantile regression procedures more accessible for researchers working with spatial data sets. The emphasis is on interpretation of quantile regression results. A series of examples using both simulated and actual data sets shows how readily seemingly complex quantile regression results can be interpreted with sets of well-constructed graphs. Both parametric and nonparametric versions of spatial models are considered in detail.

Quantile Double Autoregression

Author : Qianqian Zhu
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Quantile Double Autoregression by : Qianqian Zhu

Download or read book Quantile Double Autoregression written by Qianqian Zhu and published by . This book was released on 2019 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroscedasticity at the same time. In the meanwhile, it is still lack of a time series model to accommodate both of the above features simultaneously. This paper fills the gap by proposing a novel conditional heteroscedastic model, which is called the quantile double autoregression. The strict stationarity of the new model is derived, and a self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, two portmanteau tests are constructed, and they can be used in conjunction to check the adequacy of fitted conditional quantiles. The finite-sample performance of the proposed inference tools is examined by simulation studies, and the necessity of the new model is further demonstrated by analyzing the S &P500 Index.

Predictions in Time Series Using Regression Models

Author : Cory Terrell
Publisher : Scientific e-Resources
ISBN 13 : 1839473290
Total Pages : 300 pages
Book Rating : 4.8/5 (394 download)

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Book Synopsis Predictions in Time Series Using Regression Models by : Cory Terrell

Download or read book Predictions in Time Series Using Regression Models written by Cory Terrell and published by Scientific e-Resources. This book was released on 2019-09-02 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regression methods have been a necessary piece of time arrangement investigation for over a century. As of late, new advancements have made real walks in such territories as non-constant information where a direct model isn't fitting. This book acquaints the peruser with fresher improvements and more assorted regression models and methods for time arrangement examination. Open to any individual who knows about the fundamental present day ideas of factual deduction, Regression Models for Time Series Analysis gives a truly necessary examination of late measurable advancements. Essential among them is the imperative class of models known as summed up straight models (GLM) which gives, under a few conditions, a bound together regression hypothesis reasonable for constant, all out, and check information. The creators stretch out GLM methodology deliberately to time arrangement where the essential and covariate information are both arbitrary and stochastically reliant. They acquaint readers with different regression models created amid the most recent thirty years or somewhere in the vicinity and condense traditional and later outcomes concerning state space models.

Three Essays on Time Series Quantile Regression

Author : Yini Wang
Publisher :
ISBN 13 :
Total Pages : 308 pages
Book Rating : 4.:/5 (811 download)

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Book Synopsis Three Essays on Time Series Quantile Regression by : Yini Wang

Download or read book Three Essays on Time Series Quantile Regression written by Yini Wang and published by . This book was released on 2012 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers quantile regression models with nonstationary or nearly nonstationary time series. The first chapter outlines the thesis and discusses its theoretical and empirical contributions. The second chapter studies inference in quantile regressions with cointegrated variables allowing for multiple structural changes. The unknown break dates and regression coefficients are estimated jointly and consistently. The conditional quantile estimator has a nonstandard limit distribution. A fully modified estimator is proposed to remove the second-order bias and nuisance parameters and the resulting limit distribution is mixed normal. A simulation study shows that the fully modified quantile estimator has good finite sample properties. The model is applied to stock index data from the emerging markets of China and several mature markets. Financial market integration is found in some quantiles of the Chinese stock indices. The third chapter considers predictive quantile regression with a nearly integrated regressor. We derive nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes. The critical values are found to depend on both the quantile of interest and the local-to-unity parameter, which is not consistently estimable. Based on these critical values, we propose a valid Bonferroni bounds test for quantile predictability with persistent regressors. We employ this new methodology to test the ability of many commonly employed and highly persistent regressors, such as the dividend yield, earnings price ratio, and T-bill rate, to predict the median, shoulders, and tails of the stock return distribution. Chapter Four proposes a cumulated sum (CUSUM) test for the null hypothesis of quantile cointegration. A fully modified quantile estimator is adopted for serial correlation and endogeneity corrections. The CUSUM statistic is composed of the partial sums of the residuals from the fully modified quantile regression. Under the null, the test statistic converges to a functional of Brownian motions. In the application to U.S. interest rates of different maturities, evidence in favor of the expectations hypothesis for the term structure is found in the central part of the distributions of the Treasury bill rate and financial commercial paper rate, but in the tails of the constant maturity rate distribution.

Empirical Likelihood and Quantile Methods for Time Series

Author : Yan Liu
Publisher : Springer
ISBN 13 : 9811001529
Total Pages : 144 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Empirical Likelihood and Quantile Methods for Time Series by : Yan Liu

Download or read book Empirical Likelihood and Quantile Methods for Time Series written by Yan Liu and published by Springer. This book was released on 2018-12-05 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.