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Maddalena Cavicchioli - One of the best experts on this subject based on the ideXlab platform.
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Statistical inference for mixture GARCH models with financial application
Computational Statistics, 2021Co-Authors: Maddalena CavicchioliAbstract:In this paper we consider mixture generalized autoregressive conditional heteroskedastic models, and propose a new iteration algorithm of type EM for the estimation of model parameters. The maximum likelihood estimates are shown to be consistent, and their Asymptotic properties are investigated. More precisely, we derive simple expressions in closed form for the Asymptotic Covariance Matrix and the expected Fisher information Matrix of the ML estimator. Finally, we study the model selection and propose testing procedures. A simulation study and an application to financial real-series illustrate the results.
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A note on the Asymptotic and exact Fisher information matrices of a Markov switching VARMA process
Statistical Methods & Applications, 2020Co-Authors: Maddalena CavicchioliAbstract:We study the Asymptotic and exact Fisher information (FI) matrices of Markov switching vector autoregressive moving average (MS VARMA) models. In a related paper (2017), we propose a method to derive an explicit expression in closed form for the Asymptotic FI Matrix of the underlying model, and use such a Matrix to derive the Asymptotic Covariance Matrix of the Gaussian maximum likelihood (ML) estimator of the parameters in the MS VARMA model. In this paper, the exact FI Matrix of a Gaussian MS VARMA process is considered for a time series of length T in relation to the exact ML estimation method. Furthermore, we prove that the Gaussian exact FI Matrix converges in probability to the Asymptotic FI Matrix when the sample size T goes to infinity.
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Asymptotic fisher information Matrix of markov switching varma models
Journal of Multivariate Analysis, 2017Co-Authors: Maddalena CavicchioliAbstract:We study the Fisher information (FI) Matrix of Markov switching vector autoregressive moving average (MS VARMA) models and derive an explicit expression in closed form for the Asymptotic FI Matrix of the underlying model. Our result is more general than the available one in the literature for linear VARMA models, which has been recently studied in Bao and Hua (2014), in two respects. First, we treat the variance of the error term in a more general setting rather than considering it as a nuisance parameter. Then, we consider non-trivial intercept in the MS VARMA model. Under general conditions, the Asymptotic FI Matrix can be used to derive the Asymptotic Covariance Matrix of the Gaussian maximum likelihood estimator of the model parameters. Some examples and numerical applications illustrate the results.
Yunwei Cui - One of the best experts on this subject based on the ideXlab platform.
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a parameter driven logit regression model for binary time series
Journal of Time Series Analysis, 2014Co-Authors: Yunwei CuiAbstract:We consider a parameter-driven regression model for binary time series, where serial dependence is introduced by an autocorrelated latent process incorporated into the logit link function. Unlike in the case of parameter-driven Poisson log-linear or negative binomial logit regression model studied in the literature for time series of counts, generalized linear model (GLM) estimation of the regression coefficient vector, which suppresses the latent process and maximizes the corresponding pseudo-likelihood, cannot produce a consistent estimator. As a remedial measure, in this article, we propose a modified GLM estimation procedure and show that the resulting estimator is consistent and Asymptotically normal. Moreover, we develop two procedures for estimating the Asymptotic Covariance Matrix of the estimator and establish their consistency property. Simulation studies are conducted to evaluate the finite-sample performance of the proposed procedures. An empirical example is also presented.
Hiroyuki Kasahara - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic properties of the maximum likelihood estimator in regime switching econometric models
Journal of Econometrics, 2019Co-Authors: Hiroyuki Kasahara, Katsumi ShimotsuAbstract:Abstract Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the Asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the Asymptotic distribution of the MLE has been unknown for models in which some elements of the transition probability Matrix have the value of zero, as is commonly assumed in empirical applications with models with more than two regimes. This also includes models in which the regime-specific density depends on both the current and the lagged regimes such as the seminal model of Hamilton (1989) and switching ARCH model of Hamilton and Susmel (1994). This paper shows the Asymptotic normality of the MLE and consistency of the Asymptotic Covariance Matrix estimate of these models.
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Asymptotic properties of the maximum likelihood estimator in regime switching econometric models
Journal of Econometrics, 2019Co-Authors: Hiroyuki Kasahara, Katsumi ShimotsuAbstract:Abstract Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the Asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the Asymptotic distribution of the MLE has been unknown for models in which some elements of the transition probability Matrix have the value of zero, as is commonly assumed in empirical applications with models with more than two regimes. This also includes models in which the regime-specific density depends on both the current and the lagged regimes such as the seminal model of Hamilton (1989) and switching ARCH model of Hamilton and Susmel (1994). This paper shows the Asymptotic normality of the MLE and consistency of the Asymptotic Covariance Matrix estimate of these models.
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Asymptotic properties of the maximum likelihood estimator in regime switching econometric models
CIRJE F-Series, 2017Co-Authors: Hiroyuki Kasahara, Katsumi ShimotsuAbstract:Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the Asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the Asymptotic distribution of the MLE has been unknown for models in which the regime-specific density depends on both the current and the lagged regimes, which include the seminal model of Hamilton (1989) and the switching ARCH model of Hamilton and Susmel (1994). This paper shows the Asymptotic normality of the MLE and the consistency of the Asymptotic Covariance Matrix estimate of these models.
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Asymptotic properties of the maximum likelihood estimator in regime switching econometric models
CIRJE F-Series, 2017Co-Authors: Hiroyuki Kasahara, Katsumi ShimotsuAbstract:Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the Asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the Asymptotic distribution of the MLE has been unknown for models in which the regime-specific density depends on both the current and the lagged regimes, which include the seminal model of Hamilton (1989) and the switching ARCH model of Hamilton and Susmel (1994). This paper shows the Asymptotic normality of the MLE and the consistency of the Asymptotic Covariance Matrix estimate of these models.
Guy Melard - One of the best experts on this subject based on the ideXlab platform.
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computation of the fisher information Matrix for siso models
IEEE Transactions on Signal Processing, 1994Co-Authors: Andre Klein, Guy MelardAbstract:Closed form expressions and an algorithm for obtaining the Fisher information Matrix of Gaussian single input single output (SISO) time series models are presented. It enables the computation of the Asymptotic Covariance Matrix of maximum likelihood estimators of the parameters. The procedure makes use of the autoCovariance function of one or more autoregressive processes. Under certain conditions, the SISO model can be a special case of a vector autoregressive moving average (ARMA) model, for which there is a method to evaluate the Fisher information Matrix. That method is compared with the procedure described in the paper. >
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computation of the fisher information Matrix for siso models
ULB Institutional Repository, 1994Co-Authors: Andre Klein, Guy MelardAbstract:Closed form expressions and an algorithm for obtaining the Fisher information Matrix of Gaussian single input single output (SISO) time series models are presented. It enables the computation of the Asymptotic Covariance Matrix of maximum likelihood estimators of the parameters. The procedure makes use of the autoCovariance function of one or more autoregressive processes. Under certain conditions, the SISO model can be a special case of a vector autoregressive moving average (ARMA) model, for which there is a method to evaluate the Fisher information Matrix. That method is compared with the procedure described in the paper. © 1994 IEEE
Jinhong You - One of the best experts on this subject based on the ideXlab platform.
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empirical likelihood for semiparametric varying coefficient partially linear regression models
Statistics & Probability Letters, 2006Co-Authors: Jinhong You, Yong ZhouAbstract:This paper is concerned with the estimating problem of the varying-coefficient partially linear regression model. We apply the empirical method to this semiparametric model. An empirical log-likelihood ratio for the parametric components, which are of primary interest, is proposed and the nonparametric version of the Wilk's theorem is derived. Thus, the confidence regions of the parametric components with Asymptotically correct coverage probabilities can be constructed. Compared with those based on normal approximation, the confidence regions based on the empirical likelihood have two advantages: (1) they do not have the predetermined symmetry, which enables them to better correspond with the true shape of the underlying distribution; (2) they do not involve any Asymptotic Covariance Matrix estimation and hence are robust against the heteroscedasticity. Some simulations and an application are conducted to illustrate the proposed method.
