Theory of Partial Likelihood
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A general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood. Conditions are given for consistency and asymptotic normality, and a method is provided for the calculation of the asymptotic efficiency of the estimator. The implications of the general theory are examined in special cases such as inference in stochastic processes, Cox regression models, and AR processes with missing segments.
Normality pre-tests on reduced-form innovations cannot detect whether two or more underlying structural shocks are Gaussian, and hence cannot detect a failure of identification in non-Gaussian SVARs. We propose a bootstrap-based approach that reveals such a failure. Under the null of valid identification and certain regularity conditions, the conditional bootstrap distribution of the maximum likelihood estimator of the impact matrix is asymptotically normal, so the…
混合模型的 Whittle 似然及其地下水位时间序列应用
Understanding the processes that influence groundwater levels is crucial for forecasting and responding to hazards such as groundwater droughts. Mixed models, which combine a fixed mean, expressed using independent predictors, with autocorrelated random errors, are used for inference, forecasting and filling in missing values in groundwater level time series. Estimating parameters of mixed models using maximum likelihood has high computational complexity. For large datasets,…
基于条件异方差识别日度油价冲击及其不确定性
This paper develops a daily structural VAR for identifying oil price shocks from conditional heteroskedasticity and quantifies the transmission of their timevarying uncertainty. Identification exploits volatility clustering and spillovers in a structural GARCH specification and the complete identified set is derived. We derive covariance impulse response functions and introduce a time-varying forecast error variance decomposition (TV-FEVD) that allows for a decomposition of…
Hájek 卷积定理的二阶扩展及统计应用
For a class of regular estimators, Hájek, in his celebrated ``Convolution Theorem,'' showed that the asymptotic distribution of a regular estimator is the convolution of the distribution of an efficient estimator and some residual distribution. This result constitutes the foundation of the concept of asymptotic efficiency of regular estimators. In this paper, we provide a second-order version of that classical result. Introducing a class of second-order regular estimators…
基于正态混合准极大似然的双重自回归模型稳健估计
This paper investigates the estimation of the double autoregressive (DAR) model in the presence of skewed and heavy-tailed innovations. We propose a novel Normal Mixture Quasi-Maximum Likelihood Estimation (NM-QMLE) method to address the limitations of conventional quasi-maximum likelihood estimation (QMLE) under non-Gaussian conditions. By incorporating a normal mixture distribution into the quasi-likelihood framework, NM-QMLE effectively captures both heavy-tailed behavior…
Tensor-BEKK:张量时间序列的条件协方差建模与推断
Modern economic and financial data are increasingly organized as multiway arrays, with observations indexed simultaneously by geographic regions, industrial sectors, asset categories, and other economic characteristics. Representing such data as tensor-valued time series preserves their intrinsic multiway structure. Although substantial effort has been devoted to modeling the conditional mean of tensor-valued time series, comparatively less attention has been paid to their…