Non-parametric Econometric Methods for Continuous-time Diffusion Models PDF Download
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Author: Shin Kanaya
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Author: Shin Kanaya
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Qi Li
Publisher: Emerald Group Publishing
ISBN: 1849506248
Category : Business & Economics
Languages : en
Pages : 570
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Book Description
Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.
Author: Zhaogang Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 376
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Book Description
Continuous time Markov processes, including diffusion, jump-diffusion and Levy jump-diffusion models, have become an essential tool of modern finance over the past three decades. Nowadays, they are widely used in modeling dynamics of, for instance, interest rates, stock prices, exchange rates and option prices. However, data are always recorded at discrete points in time, e.g., monthly, weekly, and daily, although these models are formulated in continuous time. This feature makes most econometric inferential procedures developed for discrete time econometrics unsuitable for continuous time models and complicates the econometric analysis considerably. For example, estimators obtained by applying discrete time econometric methods to the discretized version of continuous time models are not consistent for a fixed sampling interval. More seriously, although the maximum likelihood method is a very appealing econometric procedure due to its nice properties like efficiency, the transition density and hence likelihood function of most continuous time Markov models have no analytic expressions. This poses a serious impediment for the implementation of likelihood procedures. Many approaches have been proposed to deal with this problem but they either incur substantive computation burdens especially for multivariate cases or involve complicated approximation formulas with limited applicability. Consequently, there is a strong need for convenient econometric methodologies designed for continuous time mod- els given discrete sampled data. Unlike the transition density, the infinitesimal operator, as an important mathematical tool in probability theory, enjoys the nice property of being a closed-form expression of drift, diffusion and jump terms of the process. As a result, no approximated formulas or simulation based implementations are needed. Furthermore, it is equivalent to the transition density in characterizing the complete dynamics of the processes. Based on this convenient infinitesimal operator, this dissertation proposes a sequence of econometric procedures for continuous time Markov models with applications to affine jump diffusion (AJD) term structure models of interest rates. It is divided into four chapters. In the first chapter, "Infinitesimal Operator Based Estimation for Continuous Time Markov Processes", I propose an estimation method based on the infinitesimal operator for general multivariate continuous-time Markov processes, which cover diffusion, jump-diffusion and Levy-driven jump models as special cases. A conditional moment restriction is first obtained via the infinitesimal operator based identification of the process. Then an empirical likelihood type estimator is constructed by a kernel smoothing approach. Unlike the transition density which is rarely available in closed-form, the infinitesimal operator has an analytic form for all continuous time Markov models. As a result, different from the maximum likelihood estimator (MLE) which involves either numerical or simulated transition densities, the proposed estimator can be conveniently implemented by plugging in parametric components of the models. Furthermore, I prove that the proposed estimator attains the semi-parametric efficiency bound for conditional moment restrictions models of Markov processes and hence is asymptotically efficient. Simulation studies show that the proposed estimator has good finite sample performances comparable to the MLE. In the empirical application, I estimate Levy jump diffusion models for daily Euro/Dollar (2000-2010) and Yen/Dollar (1990-2000) rates. Results show that Levy jumps are important components in exchange rate dynamics and Poissontype jump diffusion models cannot capture them. In the second chapter, "Expectation Puzzles, Time Varying Conditional Volatility, and Jumps in Affine Term Structure Models", I study how jumps in interest rates, which are well documented in the literature, affect the term structure dynamics of the LIBOR-Swap curve in a multivariate AJD model. The motivation is that affine diffusion (AD) term structure models, as the major framework for interest rate dynamics, face two empirical challenges: first, they ignore well-documented jumps in interest rates as the state variables follow affine diffusions; second, they fail to capture simultaneously time variations in risk premiums implied by the violations of the "expectation hypothesis" and time variations in volatilities which are critical for pricing fixed-income derivatives. In this paper, I develop a multivariate AJD term structure model that overcomes these two challenges. Using LIBOR-Swap yields from 1990 to 2008, I estimate three-factor AJD models with infinitesimal operator methods and examine the contributions of jumps to term structure dynamics. I find that jumps are state dependent and negative. The risk premium is positive for jump size risk and negative for jump time risk, while the total jump risk premium is positive. Jump risk premiums lead to flexible time-varying market prices of risks without restricting time variations in conditional volatilities. As a result, two models in the three-factor AJD class capture time variations in both the risk premium and conditional volatility of LIBOR-Swap yields simultaneously. In the third chapter (part of this chapter has been published as Song (2011) in Journal of Econometrics, 162-2, 189-212.), "A Martingale Approach for Testing Diffusion Models Based on Infinitesimal Operator", I develop an omnibus specification test for diffusion models based on the infinitesimal operator instead of the transition density extensively used in literature. The infinitesimal operator based identification of the diffusion process is equivalent to a "martingale hypothesis" for the processes obtained by a transformation of the original diffusion model. My test procedure is then constructed by checking the "martingale hypothesis" via a multivariate generalized spectral derivative based approach which delivers an N(0,1) asymptotical null distribution for the test statistic. The infinitesimal operator of the diffusion process enjoys the nice property of being a closed-form function of drift and diffusion terms. Consequently, my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case. Moreover, different transformed martingale processes contain separate information about the drift and diffusion specifications and about their interactions. This motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected. Simulation studies show that the proposed tests have reasonable size and excellent power performances. An empirical application of my test procedure using Eurodollar interest rates finds that most popular short-rate models are rejected and the drift mis-specification plays an important role in such rejections. In the fourth chapter, "Estimating Semi-Parametric Diffusion Models with Unrestricted Volatility via Infinitesimal Operator", two generalized method of moments estimators are proposed for the drift parameters in both univariate and multivariate semi-parametric diffusion models with unrestricted volatility based on the infinitesimal operator. The first estimator is obtained by integrating out the diffusion function via the quadratic variation (co-variation), which is estimated by the realized volatility (covariance) in a first step using high frequency data. The second is constructed based on the separate identification condition and is actually applicable for a general instantaneous conditional mean model in continuous time, which covers the stochastic volatility and jump diffusion models as special cases. Simulation studies show that they possess fairly good finite sample performances.
Author: Qi Li
Publisher: Princeton University Press
ISBN: 1400841062
Category : Business & Economics
Languages : en
Pages : 769
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Book Description
A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 1542
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Author: Zongwu Cai
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Yacine Ait-Sahalia
Publisher: Elsevier
ISBN: 0080929842
Category : Business & Economics
Languages : en
Pages : 809
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Book Description
This collection of original articles—8 years in the making—shines a bright light on recent advances in financial econometrics. From a survey of mathematical and statistical tools for understanding nonlinear Markov processes to an exploration of the time-series evolution of the risk-return tradeoff for stock market investment, noted scholars Yacine Aït-Sahalia and Lars Peter Hansen benchmark the current state of knowledge while contributors build a framework for its growth. Whether in the presence of statistical uncertainty or the proven advantages and limitations of value at risk models, readers will discover that they can set few constraints on the value of this long-awaited volume. Presents a broad survey of current research—from local characterizations of the Markov process dynamics to financial market trading activity Contributors include Nobel Laureate Robert Engle and leading econometricians Offers a clarity of method and explanation unavailable in other financial econometrics collections
Author: Manuel Seabra Pereira
Publisher: Springer Science & Business Media
ISBN: 1402056907
Category : Technology & Engineering
Languages : en
Pages : 605
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Book Description
This book celebrates the 75th anniversary of The Technical University of Lisbon (UTL). It provides a compelling picture of current state-of-art research at UTL. It contains the edited version of the invited lectures from a two day Symposium and brings together a comprehensive summary of high quality research contributions across basic and applied sciences. A broad spectrum of topics is covered reflecting UTL’s worldwide recognition.
Author: Terence C. Mills
Publisher: Cambridge University Press
ISBN: 1139470817
Category : Business & Economics
Languages : en
Pages : 411
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Book Description
Terence Mills' best-selling graduate textbook provides detailed coverage of research techniques and findings relating to the empirical analysis of financial markets. In its previous editions it has become required reading for many graduate courses on the econometrics of financial modelling. This third edition, co-authored with Raphael Markellos, contains a wealth of material reflecting the developments of the last decade. Particular attention is paid to the wide range of nonlinear models that are used to analyse financial data observed at high frequencies and to the long memory characteristics found in financial time series. The central material on unit root processes and the modelling of trends and structural breaks has been substantially expanded into a chapter of its own. There is also an extended discussion of the treatment of volatility, accompanied by a new chapter on nonlinearity and its testing.
Author: Jiti Gao
Publisher: CRC Press
ISBN: 1420011219
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully
