The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the ...The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the estimation of non-stationary first order TGARCH models.Restricted normal mixture quasi-maximum likelihood estimation(NM-QMLE)for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter.We show that the proposed estimators(except location parameter)are consistent and asymptotically normal under mild regular conditions.The impact of relative leptokursis and skewness of the innovations’distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed.Numerical results lend further support to our theoretical results.Finally,an illustrated real example is presented.展开更多
In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for u...In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.展开更多
The dynamic conditional correlation(DCC) model has been widely used for modeling the conditional correlation of multivariate time series by Engle(2002). However, the stationarity conditions have been established only ...The dynamic conditional correlation(DCC) model has been widely used for modeling the conditional correlation of multivariate time series by Engle(2002). However, the stationarity conditions have been established only recently and the asymptotic theory of parameter estimation for the DCC model has not yet to be fully discussed. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation(SDCC) model. Sufficient and easily-checked conditions for stationarity, geometric ergodicity, andβ-mixing with exponential-decay rates are provided. We then show the strong consistency and asymptotic normality of the quasi-maximum-likelihood estimator(QMLE) of the model parameters under regular conditions.The asymptotic results are illustrated by Monte Carlo experiments. As a real-data example, the proposed SDCC model is applied to analyzing the daily returns of the FSTE(financial times and stock exchange) 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the Li-Mc Leod statistic of the SDCC model is much smaller and the hedging efficiency is higher.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11101448)the Program for New Century Excellent Talents in University+3 种基金the Program for Young Talents of Beijing (Grant No.YETP0955)the Program for National Statistics Science Research Plan (Grant No.2013LY015)the "Project 211" of the Central University of Finance and Economicsthe Central University of Finance Young Scholar Innovation Fund
文摘The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the estimation of non-stationary first order TGARCH models.Restricted normal mixture quasi-maximum likelihood estimation(NM-QMLE)for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter.We show that the proposed estimators(except location parameter)are consistent and asymptotically normal under mild regular conditions.The impact of relative leptokursis and skewness of the innovations’distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed.Numerical results lend further support to our theoretical results.Finally,an illustrated real example is presented.
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.
基金supported by National Natural Science Foundation of China(Grant No.71771224)National Social Science Foundation of China(Grant Nos.14ZDA044 and 15BGJ037)+1 种基金the Program for National Statistics Science Research Plan(Grant No.2016LD02)the Program for Innovation Research in Central University of Finance and Economics
文摘The dynamic conditional correlation(DCC) model has been widely used for modeling the conditional correlation of multivariate time series by Engle(2002). However, the stationarity conditions have been established only recently and the asymptotic theory of parameter estimation for the DCC model has not yet to be fully discussed. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation(SDCC) model. Sufficient and easily-checked conditions for stationarity, geometric ergodicity, andβ-mixing with exponential-decay rates are provided. We then show the strong consistency and asymptotic normality of the quasi-maximum-likelihood estimator(QMLE) of the model parameters under regular conditions.The asymptotic results are illustrated by Monte Carlo experiments. As a real-data example, the proposed SDCC model is applied to analyzing the daily returns of the FSTE(financial times and stock exchange) 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the Li-Mc Leod statistic of the SDCC model is much smaller and the hedging efficiency is higher.
