Download or read book Asymptotic Results for GMM Estimators of Stochastic Volatility Models written by Geert Dhaene and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotics for GMM Estimators with Weak Instruments written by James H. Stock and published by . This book was released on 1996 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments. The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentrated) objective function as a stochastic process. The general results are specialized to two leading cases, linear instrumental variables regression and GMM estimation of Euler equations obtained from the consumption-based capital asset pricing model with power utility. Numerical results of the latter model confirm that finite sample distributions can deviate substantially from normality, and indicate that these deviations are captured by the weak instrument asymptotic approximations.

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.

Download or read book IV and GMM Estimation and Testing of Multivariate Stochastic Unit Root Models written by Offer Lieberman and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lieberman and Phillips (2016; Journal of Econometrics; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which conveniently addresses endogeneity. We derive the asymptotic distributions of the NLIV and GMM estimators and establish consistency under similar orthogonality and relevance conditions to those used in the linear model. An overidentification test and its asymptotic distribution are also developed. The results enable inference about structural STUR models and a mechanism for testing the local STUR model against a simple UR null, which complements usual UR tests. Simulations reveal that the asymptotic distributions of the the NLIV and GMM estimators of the STUR parameter as well as the test for overidentifying restrictions perform well in small samples and that the distribution of the NLIV estimator is heavily leptokurtic with a limit theory which has Cauchy-like tails. Comparisons of STUR coefficient and a standard UR coefficient test show that the one-sided UR test performs poorly against the one-sided STUR coefficient test both as the sample size and departures from the null rise.

Download or read book Handbook of Economic Forecasting written by G. Elliott and published by Elsevier. This book was released on 2006-07-14 with total page 1071 pages. Available in PDF, EPUB and Kindle. Book excerpt: Section headings in this handbook include: 'Forecasting Methodology; 'Forecasting Models'; 'Forecasting with Different Data Structures'; and 'Applications of Forecasting Methods.'.

Download or read book Spectral GMM Estimation of Continuous Time Processes written by George Chacko and published by . This book was released on 2009 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a methodology for the exact estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the process, and it is easy to apply. The method is essentially generalized method of moments on the complex plane. Hence it shares the optimality and distribution properties of GMM estimators. Moreover, we show that there are instruments that make the estimator asymptotically efficient. We illustrate the method with some applications to relevant estimation problems in continuous-time finance. We estimate a model of stochastic volatility, a jump-diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump-diffusion model. We find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution, while stochastic volatility is important to capture the overall level of this kurtosis. Positive jumps are not statistically significant once we allow for stochastic volatility in the model. We also estimate a non-affine model of stochastic volatility and we find that the power of the diffusion coefficient appears to be between one and two, rather than the value of one-half that leads to the standard affine stochatic volatility model. Finally, we offer an explanation for the observation that the estimate of persistence in stochatic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model.

Download or read book Journal of Econometrics written by and published by . This book was released on 2002 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility Models written by Jian Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book GMM Estimation of a Stochastic Volatility Model written by Torben G. Andersen and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the properties of alternative GMM procedures for estimation of the log-normal stochastic autoregessive volatility model through a large scale Monte Carlo study. We demonstrate that there is a fundamental trade-off between the number of moments, or information, included in the estimation, and the quality, or precision of the objective function used for estimation. Furthermore, a large sample approximation of the optimal weighting matrix is used to explore the impact of the weighting matrix in the estimation procedure and to obtain practical efficiency bounds for the given class of GMM estimators. Most importantly, we find that the best inference is obtained by including a lower number of moments in the GMM procedure than is often used in practical applications. Further, when an excessive number of moments is used, the chi-squared statistic is strongly downward biased, leading to a serious size distortion. For large samples, we make the specific recommendation of using the Newey and West (1993) procedure based on the Bartlett kernel and their specific data-dependent bandwidth.

Download or read book The Asymptotic Properties of the System GMM Estimator in Dynamic Panel Data Models When Both N and T are Large written by Kazuhiko Hayakawa and published by . This book was released on 2014 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive the asymptotic properties of the system GMM estimator in dynamic panel data models with individual and time effects when both N and T, the dimensions of cross section and time series, are large. We first show that the two-step level GMM estimator with an optimal weighting matrix is consistent under large N and T asymptotics, whereas that with a non-optimal one is not. We then show that the two-step system GMM estimator is consistent even if a sub-optimal weighting matrix where off-diagonal blocks are set to zero is used. Such consistency results theoretically support the use of the system GMM estimator in large N and T contexts even though it was originally developed for large N and small T panels. Simulation results indicate that the large N and large T asymptotic results approximate the finite sample behavior reasonably well unless persistency of data is strong and/or the variance ratio of individual effects to the disturbances is large.

Download or read book Handbook of Financial Econometrics written by Yacine Ait-Sahalia and published by Elsevier. This book was released on 2009-10-19 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Statistical Inference for Stochastic Volatility Models written by Md. Nazmul Ahsan and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Although stochastic volatility (SV) models have many appealing features, estimation and inference on SV models are challenging problems due to the inherent difficulty of evaluating the likelihood function. The existing methods are either computationally costly and/or inefficient. This thesis studies and contributes to the SV literature from the estimation, inference, and volatility forecasting viewpoints. It consists of three essays, which include both theoretical and empirical contributions. On the whole, the thesis develops easily applicable statistical methods for stochastic volatility models.The first essay proposes computationally simple moment-based estimators for the first-order SV model. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that the proposed estimators match (or exceed) alternative estimators in terms of precision – including Bayesian estimators proposed in this context, which have the best performance among alternative estimators. Using this simple estimator, we study three crucial test problems (no persistence, no latent specification of volatility, and no stochastic volatility hypothesis), and evaluate these null hypotheses in three ways: asymptotic critical values, a parametric bootstrap procedure, and a maximized Monte Carlo procedure. The proposed methods are applied to daily observations on the returns for three major stock prices [Coca-Cola, Walmart, Ford], and the Standard and Poor’s Composite Price Index. The results show the presence of stochastic volatility with strong persistence.The second essay studies the problem of estimating higher-order stochastic volatility [SV(p)] models. The estimation of SV(p) models is even more challenging and rarely considered in the literature. We propose several estimators for higher-order stochastic volatility models. Among these, the simple winsorized ARMA-based estimator is uniformly superior in terms of bias and RMSE to other estimators, including the Bayesian MCMC estimator. The proposed estimators are applied to stock return data, and the usefulness of the proposed estimators is assessed in two ways. First, using daily returns on the S&P 500 index from 1928 to 2016, we find that higher-order SV models – in particular an SV(3) model – are preferable to an SV(1), from the viewpoints of model fit and both asymptotic and finite-sample tests. Second, using different volatility proxies (squared return and realized volatility), we find that higher-order SV models are preferable for out-of-sample volatility forecasting, whether a high volatility period (such as financial crisis) is included in the estimation sample or the forecasted sample. Our results highlight the usefulness of higher-order SV models for volatility forecasting.In the final essay, we introduce a novel class of generalized stochastic volatility (GSV) models which utilize high-frequency (HF) information (realized volatility (RV) measures). GSV models can accommodate nonstationary volatility process, various distributional assumptions, and exogenous regressors in the latent volatility equation. Instrumental variable methods are employed to provide a unified framework for the analysis (estimation and inference) of GSV models. We consider the parameter inference problem in GSV models with nonstationary volatility and develop identification-robust methods for joint hypotheses involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For distributional theory, three different sets of assumptions are considered. In simulations, the proposed tests outperform the usual asymptotic test regarding size and exhibit excellent power. We apply our inference methods to IBM price and option data andidentify several empirical relationships"--

Download or read book Asymptotic Behavior of Stochastic Volatility Models written by Max Souza and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Method of Moments Estimation written by Laszlo Matyas and published by Cambridge University Press. This book was released on 1999-04-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized method of moments (GMM) estimation has emerged as providing a ready to use, flexible tool of application to a large number of econometric and economic models by relying on mild, plausible assumptions. The principal objective of this volume is to offer a complete presentation of the theory of GMM estimation as well as insights into the use of these methods in empirical studies. It is also designed to serve as a unified framework for teaching estimation theory in econometrics. Contributors to the volume include well-known authorities in the field based in North America, the UK/Europe, and Australia. The work is likely to become a standard reference for graduate students and professionals in economics, statistics, financial modeling, and applied mathematics.

Download or read book Realized Stochastic Volatility with General Asymmetry and Long Memory written by Manabu Asai and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann's seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyses the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

Download or read book Asymptotic Analysis for a Simple Explicit Estimator in Barndorff Nielsen and Shephard Stochastic Volatility Models written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book GMM Estimation of a Stochastic Volatility Model with Realized Volatility a Monte Carlo Study written by Pierre Chaussé and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: