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Three Econometric Essays On Continuous Time Models

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Three Econometric Essays On Continuous Time Models

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Author : Xiaohu Wang
language : en
Publisher:
Release Date : 2012

Three Econometric Essays On Continuous Time Models written by Xiaohu Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Asymptotic distribution (Probability theory) categories.

"Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. The chapter 2 introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that for plausible parameter settings the approximation methods work better than ML, the bias formulae are accurate, and the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman's method and the Milstein method. The Chapter 3 examines the asymptotic properties of the maximum likelihood (ML) estimate of the mean reversion matrix that is obtained from the corresponding exact discrete model. Both the consistency and the asymptotic distribution are derived in the cases of stationarity and non-stationarity . Special attention is paid to the explicit expressions for the asymptotic covariance matrix, especially in low dimensional cases. This limit theory is facilitated by a new formula for the mapping from the discrete to the continuous system coefficients and its derivatives. An empirical application is conducted on daily realized volatility data on Pound, Euro and Yen exchange rates, illustrating the implementation of the theory. Recently, with the coming of the financial crisis, the interest of using explosive process to model asset bubbles has been growing tremendously. This underlies the importance of statistic properties of the explosive process. The Chapter 4 develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Levy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a technique in the same spirit as in Phillips and Magdalinos (2007) for the mildly explosive discrete time model. Both the intercept term and the initial condition appear in the limiting distribution. In the special case of explosive continuous time models driven by the Brownian motion, we develop the limit theory that allows for the joint limits where N 2 and h 2 0 simultaneously, the sequential limits N 2 is followed by h 2 0, and the sequential limits where h 2 0 is followed by N 2 . All three asymptotic distributions are the same."--Author's abstract.

Three Essays On Continuous Time Diffusion Models

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Author : Seungmoon Choi
language : en
Publisher:
Release Date : 2005

Three Essays On Continuous Time Diffusion Models written by Seungmoon Choi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Continuous Time Econometrics

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Author : G. Gandolfo
language : en
Publisher: Springer Science & Business Media
Release Date : 1993

Continuous Time Econometrics written by G. Gandolfo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Business & Economics categories.

Time elapses continuously not in discrete jumps of, say, a quarter or a month. Hence models specified in continuous time are more realistic than the usual models in which time is taken to elapse in such discrete jumps. However much data available to economists is of the discrete-time kind. This was once thought to render impossible the econometric estimation of continuous time models. Over the past decade a body of theory has been built up to show that such estimation is not only possible but has serious practical applications. This collection of essays aims to provide not only the latest developments in the theory but also with original examples to show how it is possible to implement in real situations. Econometricians may find this book useful reading as may those concerned with macroeconomic issues who wish to keep in touch with the "frontiers" of their subject.

Three Essays On Trend Analysis And Misspecification In Structural Econometric Models

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Author :
language : en
Publisher:
Release Date : 2003

Three Essays On Trend Analysis And Misspecification In Structural Econometric Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

The purpose of this research has been to look into several econometric issues of concern to researchers doing applied work in macroeconomics. The first essay looks at Bureau of Economic Analysis data on inventories and sales of finished goods often used in studies of inventory behavior. Applying recently developed methods, the series are rigorously tested to determine their stationarity properties. Results indicate that neither first differencing nor linearly detrending the data is appropriate. For most series a trend function with one or more breaks offers a better fit and also generates stationarity. The results are used to determine the impact on estimation in a simple production-smoothing model of inventory behavior. The impact of different trend specifications on univariate forecasting of inventories is also considered. The second essay considers an alternative method of detrending time series data -- the Hodrick-Prescott (HP) filter. Previous research has shown that HP filtering can have serious adverse consequences when used to analyze co-movements between data series at business cycle frequencies. Despite this, the filter has also been used to induce stationarity in a data series prior to estimation of structural econometric models. Little work has been done in analyzing the possible effects this may have on parameter estimates from such models. A simulation study is conducted to assess the impact of HP filtering on parameter estimation and a comparison is made to other detrending methods. It is shown that the HP filter induces bias in the parameter estimates and also increases the root mean squared error of the estimates from the simulations. In addition, there is some adverse impact on the size of certain test statistics. The final essay looks at the impact of misspecification on estimation results from a structural econometric model when using a Generalized Method of Moments estimator. Simulated data consistent with a particular specification of the.

Essays In Nonlinear Time Series Econometrics

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Author : Niels Haldrup
language : en
Publisher: Oxford University Press, USA
Release Date : 2014-05

Essays In Nonlinear Time Series Econometrics written by Niels Haldrup and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05 with Business & Economics categories.

A book on nonlinear economic relations that involve time. It covers specification testing of linear versus non-linear models, model specification testing, estimation of smooth transition models, volatility modelling using non-linear model specification, analysis of high dimensional data set, and forecasting.

Continuous Time Econometric Modelling

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Author : Abram R. Bergstrom
language : en
Publisher: Oxford University Press, USA
Release Date : 1990

Continuous Time Econometric Modelling written by Abram R. Bergstrom and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Business & Economics categories.

Continuous time econometric models require very sophisticated methods and the difficulties involved in these methods have heretofore inhibited the use of the models. In this volume, Bergstrom aims to convince the non-specialist of the applicability of his models to current data. The book is concerned with a new and more realistic type of econometric model in which the economy is assumed to be adjusting continuously rather than at regular intervals of time, e.g. quarterly or annually. The book is divided into three sections. Part I looks at theoretical models of cyclical growth which have provided the basis for much of the applied work on continuous time macroeconometric models. Part II is concerned with econometric methodology and includes papers on estimation, testing, forecasting, and optimal control. Part III is concerned with applications and includes material on the well-known Bergstrom-Wymer continuous time macroeconomic model of the United Kingdom.