Adaptive Estimation in Multiple Time Series With Independent Component Errors
针对高维多变量时间序列，提出一种半参数自适应估计方法，在无需完全参数化创新分布的情况下，获得比高斯伪极大似然估计更有效的参数估计，并通过蒙特卡洛模拟验证了有限样本性能。
This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N . The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross‐autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non‐identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo‐maximum likelihood estimates of the parameters are typically √ n ‐consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call ‘adaptive,’ are asymptotically as first‐order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel‐based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √ n ‐consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing a variety of parameterizations, distributions and choices of N , is reported.