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Quantile Based Inference For Tempered Stable Distributions
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Book Synopsis Quantile-Based Inference for Tempered Stable Distributions by : Hasan Fallahgoul
Download or read book Quantile-Based Inference for Tempered Stable Distributions written by Hasan Fallahgoul and published by . This book was released on 2016 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: If the closed-form formula for the probability density function is not available, implementing the maximum likelihood estimation is challenging. We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the Method of Simulated Quantiles (Dominicy and Veredas (2013)). MSQ consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than Maximum Likelihood and the estimates are almost as precise as MLE. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that MSQ estimates provide as good risk assessments as with MLE.
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.
Book Synopsis Robust Inference with Quantile Regression in Stochastic Volatility Models with Application to Value at Risk Calculation by :
Download or read book Robust Inference with Quantile Regression in Stochastic Volatility Models with Application to Value at Risk Calculation written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Volatility (SV) models play an integral role in modeling time varying volatility, with widespread application in finance. Due to the absence of a closed form likelihood function, estimation is a challenging problem. In the presence of outliers, and the high kurtosis prevalent in financial data, robust estimation techniques are desirable. Also, in the context of risk assessment when the underlying model is SV, computing the one step ahead predictive return densities for Value at Risk (VaR) calculation entails a numerically indirect procedure. The Quantile Regression (QR) estimation is an increasingly important tool for analysis, which helps in fitting parsimonious models in lieu of full conditional distributions. We propose two methods (i) Regression Quantile Method of Moments (RQMM) and (ii) Regression Quantile - Kalman Filtering method (RQ-KF) based on the QR approach that can be used to obtain robust SV model parameter estimates as well as VaR estimates. The RQMM is a simulation based indirect inference procedure where auxiliary recursive quantile models are used, with gradients of the RQ objective function providing the moment conditions. This was motivated by the Efficient Method of Moments (EMM) approach used in SV model estimation and the Conditional Autoregressive Value at Risk (CAViaR) method. An optimal linear quantile model based on the underlying SV assumption is derived. This is used along with other CAViaR specifications for the auxiliary models. The RQ-KF is a computationally simplified procedure combining the QML and QR methodologies. Based on a recursive model under the SV framework, quantile estimates are produced by the Kalman filtering scheme and are further refined using the RQ objective function, yielding robust estimates. For illustration purposes, comparison of the RQMM method with EMM under different data scenarios show that RQMM is stable under model misspecification, presence of outliers and heavy-tailedness. Comparison of the RQ.
Book Synopsis Quantile Processes with Statistical Applications by : Miklos Csorgo
Download or read book Quantile Processes with Statistical Applications written by Miklos Csorgo and published by SIAM. This book was released on 1983-01-01 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.
Book Synopsis Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks by : Victor Chernozhukov
Download or read book Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks written by Victor Chernozhukov and published by . This book was released on 2011 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile regression applied to the tails, is of interest in many economic and financial applications, such as conditional value-at-risk, production efficiency, and adjustment bands in (S, s) models. In this paper we provide feasible inference tools for extremal conditional quantile models that rely upon extreme value approximations to the distribution of self-normalized quantile regression statistics. The methods are simple to implement and can be of independent interest even in the non-regression case. We illustrate the results with two empirical examples analyzing extreme fluctuations of a stock return and extremely low percentiles of live infants' birth weights in the range between 250 and 1500 grams.
Book Synopsis Fundamental Statistical Inference by : Marc S. Paolella
Download or read book Fundamental Statistical Inference written by Marc S. Paolella and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
Book Synopsis New Theory and Methods for High-Order Accurate Inference on Quantile Treatment Effects and Conditional Quantiles by : David M. Kaplan
Download or read book New Theory and Methods for High-Order Accurate Inference on Quantile Treatment Effects and Conditional Quantiles written by David M. Kaplan and published by . This book was released on 2013 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concerns methods for inference on quantiles in various models. Methods that are asymptotically justified may still be quite inaccurate in finite samples. To improve the state of the art, I explore different theoretical approaches for achieving higher-order accuracy: fractional order statistic theory based on exact finite-sample distributions in Chapters 1 and 2, and Edgeworth expansions and fixed-smoothing asymptotics in Chapter 3. For each of the different practical methods proposed, I examine accuracy via precise theoretical results as well as simulations. The family of methods using interpolated duals of exact-analytic L-statistics (IDEAL) covers unconditional (one-sample and two-sample treatment/control, Ch. 1) and nonparametric conditional (Ch. 2) models, and it offers improvements over the existing literature in terms of accuracy, robustness, and/or computation time. The Edgeworth-based method improves upon related prior methods and is a good alternative for quantiles too far into the tails for IDEAL to handle.
Book Synopsis Distribution-free Inference about Quantiles by : J. W. Snow
Download or read book Distribution-free Inference about Quantiles written by J. W. Snow and published by . This book was released on 1972 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Conditional Quantile Processes Based on Series Or Many Regressors by : Alexandre Belloni
Download or read book Conditional Quantile Processes Based on Series Or Many Regressors written by Alexandre Belloni and published by . This book was released on 2011 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantile-specific coefficients and estimate the function-valued coefficients from the data. We develop large sample theory for the empirical QR coefficient process, namely we obtain uniform strong approximations to the empirical QR coefficient process by conditionally pivotal and Gaussian processes, as well as by gradient and weighted bootstrap processes. We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence, large sample distributions, and inference methods based on strong pivotal and Gaussian approximations and on gradient and weighted bootstraps. All of the above results are for function-valued parameters, holding uniformly in both the quantile index and in the covariate value, and covering the pointwise case as a by-product. If the function of interest is monotone, we show how to use monotonization procedures to improve estimation and inference. We demonstrate the practical utility of these results with an empirical example, where we estimate the price elasticity function of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption. Keywords: quantile regression series processes, uniform inference. JEL Classifications: C12, C13, C14.
Book Synopsis Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes by : Victor Chernozhukov
Download or read book Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes written by Victor Chernozhukov and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a method to construct simultaneous confidence bands for quantile and quantile effect functions for possibly discrete or mixed discrete-continuous random variables. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling strategies and does not depend on the sampling schemes. It is based upon projection of simultaneous confidence bands for distribution functions. We apply our method to analyze the distributional impact of insurance coverage on health care utilization and to provide a distributional decomposition of the racial test score gap. Our analysis generates new interesting findings, and complements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering standard inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.
Book Synopsis Statistical Inference of Conditional Quantiles in Nonlinear Time Series Models by : Mike K. P. So
Download or read book Statistical Inference of Conditional Quantiles in Nonlinear Time Series Models written by Mike K. P. So and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the statistical properties of a two-step conditional quantile estimator in nonlinear time series models with unspecified error distribution. The asymptotic distribution of the quasi-maximum likelihood estimators and the filtered empirical percentiles is derived. Three applications of the asymptotic result are considered. First, we construct an interval estimator of the conditional quantile without any distributional assumptions. Second, we develop a specification test for the error distribution. Finally, using the specification test, we propose methods for estimating the tail index of the error distribution that would support the construct of a new high conditional quantile estimator. The asymptotic results and their applications are illustrated by simulations and real data analyses in which our methods for analyzing daily and intraday financial return series have been adopted.
Book Synopsis Quantile-based Methods for Prediction, Risk Measurement and Inference by : Abdallah K. Ally
Download or read book Quantile-based Methods for Prediction, Risk Measurement and Inference written by Abdallah K. Ally and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Book Synopsis Quantiles, Parametric-Select Density Estimations, and Bi-Information Parameter Estimators by : Emanuel Parzen
Download or read book Quantiles, Parametric-Select Density Estimations, and Bi-Information Parameter Estimators written by Emanuel Parzen and published by . This book was released on 1982 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper outlines a quantile-based approach to functional inference problems in which the parameters to be estimated are density functions. Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models. (Author).
Book Synopsis Exact Inference in Predictive Quantile Regressions with an Application to Stock Returns by : Sermin Gungor
Download or read book Exact Inference in Predictive Quantile Regressions with an Application to Stock Returns written by Sermin Gungor and published by . This book was released on 2017 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop an exact and distribution-free procedure to test for quantile predictability at several quantile levels jointly, while allowing for an endogenous predictive regressor with any degree of persistence. The approach proceeds by combining together the quantile regression t-statistics from each considered quantile level and uses Monte Carlo resampling techniques to control the overall significance level of the data-dependent combination in finite samples. A simulation study confirms the fact that the proposed inference procedure controls the familywise error rate and achieves good power. We use the new approach to test the ability of many commonly used variables to predict the quantiles of excess stock returns, and shed new light on tail predictability.
Book Synopsis Finite Sample Inference for Quantile Regression Models by : Victor Chernozhukov
Download or read book Finite Sample Inference for Quantile Regression Models written by Victor Chernozhukov and published by . This book was released on 2006 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference for both linear and nonlinear quantile models regardless of whether the covariates are endogenous or exogenous. The confidence regions can be computed using MCMC, and confidence bounds for single parameters of interest can be computed through a simple combination of optimization and search algorithms. We illustrate the finite sample procedure through a brief simulation study and two empirical examples: estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling. In all cases, we find pronounced differences between confidence regions formed using the usual asymptotics and confidence regions formed using the finite sample procedure in cases where the usual asymptotics are suspect, such as inference about tail quantiles or inference when identification is partial or weak. The evidence strongly suggests that the finite sample methods may usefully complement existing inference methods for quantile regression when the standard assumptions fail or are suspect. Keywords: Quantile Regression, Extremal Quantile Regression, Instrumental Quantile Regression. JEL Classifications: C1, C3.
Book Synopsis Limiting Distributions of Moment- and Quantile-based Measures for Skewness and Kurtosis by : J. J. A. Moors
Download or read book Limiting Distributions of Moment- and Quantile-based Measures for Skewness and Kurtosis written by J. J. A. Moors and published by . This book was released on 1993 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
