By employing the empirical likelihood method, confidence regions for the stationary AR（p）-ARCH（q） models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-li...By employing the empirical likelihood method, confidence regions for the stationary AR（p）-ARCH（q） models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained. Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy, especially for relative small size of observation.展开更多
Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed ...Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-展开更多
In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction...In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities (No. 2010LKSX04)Supported by the National Natural Science Foundation of China (No. 10731010)
文摘By employing the empirical likelihood method, confidence regions for the stationary AR（p）-ARCH（q） models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained. Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy, especially for relative small size of observation.
文摘Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-
文摘In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.
