The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Michael Mcaleer - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes
2016Co-Authors: Manabu Asai, Michael McaleerAbstract:The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated Asymptotic Theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive Asymptotic Theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated Asymptotic properties.
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Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes
2016Co-Authors: Manabu Asai, Michael McaleerAbstract:textabstractThe paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated Asymptotic Theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive Asymptotic Theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated Asymptotic properties.
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A general Asymptotic Theory for time‐series models
Statistica Neerlandica, 2010Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper develops a general Asymptotic Theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the Asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.
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A General Asymptotic Theory for Time Series Models
CIRJE F-Series, 2009Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper develops a general Asymptotic Theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the Asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.
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Asymptotic Theory for a vector arma garch model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the Asymptotic Theory for a vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi- maximum likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH and GARCH models. Moreover, the Asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the Asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models, as well as a consistent estimator of the Asymptotic covariance.
Weilin Xiao - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic Theory for rough fractional Vasicek models
Economics Letters, 2019Co-Authors: Weilin XiaoAbstract:Abstract This paper extends the Asymptotic Theory for the fractional Vasicek model developed in Xiao and Yu (2018) from the case where H ∈ ( 1 ∕ 2 , 1 ) to where H ∈ ( 0 , 1 ∕ 2 ) . It is found that the Asymptotic Theory of the persistence parameter ( κ ) critically depends on the sign of κ . Moreover, if κ > 0 , the Asymptotic distribution for the estimator of κ is different when H ∈ ( 0 , 1 ∕ 2 ) from that when H ∈ ( 1 ∕ 2 , 1 ) .
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Asymptotic Theory for estimating drift parameters in the fractional Vasicek model
Econometric Theory, 2018Co-Authors: Weilin XiaoAbstract:This paper develops the Asymptotic Theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the Asymptotic Theory for the persistent parameter depends critically on its sign, corresponding Asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered. When the persistent parameter is positive, the estimate method of Hu and Nualart (2010) is also considered. The strong consistency and the Asymptotic distribution are obtained in all three cases.
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Asymptotic Theory for estimating drift parameters in the fractional Vasicek model
Econometric Theory, 2018Co-Authors: Weilin XiaoAbstract:This article develops an Asymptotic Theory for estimators of two parameters in the drift function in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model with long-range dependence is assumed to be driven by a fractional Brownian motion with the Hurst parameter greater than or equal to one half. It is shown that, when the Hurst parameter is known, the Asymptotic Theory for the persistence parameter depends critically on its sign, corresponding Asymptotically to the stationary case, the explosive case, and the null recurrent case. In all three cases, the least squares method is considered, and strong consistency and the Asymptotic distribution are obtained. When the persistence parameter is positive, the estimation method of Hu and Nualart ( 2010 ) is also considered.
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Asymptotic Theory for Rough Fractional Vasicek Models
2018Co-Authors: Weilin XiaoAbstract:This paper extends the Asymptotic Theory for the fractional Vasicek model developed in Xiao and Yu (2018) from the case where H ∈ (1/2, 1) to the case where H ∈ (0, 1/2). It is found that the Asymptotic Theory of the persistence parameter (k) critically depends on the sign of k. Moreover, if k > 0, the Asymptotic distribution for the estimator of k is different when H ∈ (0, 1/2) from that when H ∈ (1/2, 1).
Shiqing Ling - One of the best experts on this subject based on the ideXlab platform.
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A general Asymptotic Theory for time‐series models
Statistica Neerlandica, 2010Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper develops a general Asymptotic Theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the Asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.
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A General Asymptotic Theory for Time Series Models
CIRJE F-Series, 2009Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper develops a general Asymptotic Theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the Asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.
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Asymptotic Theory for a vector arma garch model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the Asymptotic Theory for a vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder moments of the model are established. Consistency of the quasi- maximum likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate ARCH and GARCH models. Moreover, the Asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors, and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the Asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models, as well as a consistent estimator of the Asymptotic covariance.
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Asymptotic Theory for a vector arma garch model
Econometric Theory, 2003Co-Authors: Shiqing Ling, Michael McaleerAbstract:This paper investigates the Asymptotic Theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity (ARCH) and GARCH models. Moreover, the Asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors. Under additional moment conditions, the Asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models and also a consistent estimator of the Asymptotic covariance. The authors thank the co-Editor, Bruce Hansen, and two referees for very helpful comments and suggestions and acknowledge the financial support of the Australian Research Council.
Sergio Bittanti - One of the best experts on this subject based on the ideXlab platform.
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Assessing the quality of identified models through the Asymptotic Theory-when is the result reliable?
Automatica, 2004Co-Authors: Simone Garatti, Marco C. Campi, Sergio BittantiAbstract:In this paper, the problem of estimating uncertainty regions for identified models is considered. A typical approach in this context is to resort to the Asymptotic Theory of Prediction Error Methods for system identification, by means of which ellipsoidal uncertainty regions can be constructed for the uncertain parameters. We show that the uncertainty regions worked out through the Asymptotic Theory can be unreliable in certain situations, precisely characterized in the paper. Then, we critically analyze the theoretical conditions for the validity of the Asymptotic Theory, and prove that the Asymptotic Theory also applies under new assumptions which are less restrictive than the usually required ones. Thanks to this result, we single out the classes of models among standard ones (ARX, ARMAX, Box-Jenkins, etc.) where the Asymptotic Theory can be safely used in practical applications to assess the quality of the identified model. These results are of interest in many applications, including iterative controller design schemes.
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Model quality assessment for instrumental variable methods: use of the Asymptotic Theory in practice
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 1Co-Authors: Simone Garatti, Marco C. Campi, Sergio BittantiAbstract:In this paper the problem of computing uncertainty regions for models identified through an instrumental variable technique is considered. Recently, it has been pointed out that, in certain operating conditions, the Asymptotic Theory of system identification (the most widely used method for model quality assessment) may deliver unreliable confidence regions. The aim of this paper is to show that, in an instrumental variable setting, the Asymptotic Theory exhibits a certain "robustness" that makes it reliable even when used with moderate data samples. Reasons for this are highlighted in the paper through a theoretical analysis and simulation examples.
Masanobu Taniguchi - One of the best experts on this subject based on the ideXlab platform.
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Lan Based Asymptotic Theory for Time Series
Calcutta Statistical Association Bulletin, 2002Co-Authors: Masanobu Taniguchi, Madan L. PuriAbstract:The local Asymptotic normality (LAN) , introduced by LeCam, is the most fundamental concept in the statistical Asymptotic Theory. If LAN property for a class of statistical models is established, then the Asymptotic optimality of estimator and test can be described in terms of the central sequence. This concept gives a unified view for the statistical estimation and testing Theory. Recently the LAN concept has been introduced to the Asymptotic Theory for time series. This paper provides a personal overview of the LAN results for linear processes, nonlinear processes, diffusion processes, long-memory processes, and locally stationary processes, etc.. The results are applied to the Asymptotic estimation, testing Theory, and discriminant analysis in time series. Then, construction of Asymptotically optimal estimator, test and discriminator is discussed.
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Asymptotic Theory of Estimation and Testing for Stochastic Processes
Asymptotic Theory of Statistical Inference for Time Series, 2000Co-Authors: Masanobu Taniguchi, Yoshihide KakizawaAbstract:In classical time series analysis the Asymptotic estimation and testing Theory was developed for linear processes, which include the AR, MA, and ARMA models. However, in the last twenty years a lot of more complicated stochastic process models have been introduced, such as, nonlinear time series models, diffusion processes, point processes, and nonergodic processes. This chapter is devoted to providing a modern Asymptotic estimation and testing Theory for those various stochastic process models. The approach is mainly based on the LAN results given in the previous chapter. More concretely, in Section 3.1 we discuss the Asymptotic estimation and testing Theory for non-Gaussian vector linear processes in view of LAN. The results are very general and grasp a lot of other works dealing with AR, MA, and ARMA models as special cases. Section 3.2 reviews some elements of nonlinear time series models and the Asymptotic estimation Theory based on the conditional least squares estimator and maximum likelihood estimator (MLE). We address the problem of statistical model selection in general fashion. Also the Asymptotic Theory for nonergodic models is mentioned. Recently much attention has been paid to continuous time processes (especially diffusion processes), which appear in finance. Hence, in Section 3.3 we describe the foundation of stochastic integrals and diffusion processes. Then the LAN-based Asymptotic Theory of estimation for them is studied.
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A Survey of the First-Order Asymptotic Theory for Time Series Analysis
Higher Order Asymptotic Theory for Time Series Analysis, 1991Co-Authors: Masanobu TaniguchiAbstract:In this chapter we give a brief review of the first-order Asymptotic Theory for time series analysis and a motivation for the higher order Asymptotic Theory.
