论文检索

长记忆时间序列的离散傅里叶变换相关矩阵与大型 Toeplitz 系统快速求解AI 解读

We show that for long-memory time series, the Toeplitz system Σn(f)x = b can be solved in O(nlog5/2n) operations using a well-known version of the preconditioned conjugate gradient method, where Σn(f) is the n × n covariance matrix, f is the spectral density, and b is a known vector. Solutions of such systems are needed for optimal linear prediction and interpolation. We establish connections between this preconditioning method and the frequency domain analysis of time…

多元分数协整的半参数估计AI 解读

We consider the semiparametric estimation of fractional cointegration in a multivariate process of cointegrating rank r > 0. We estimate the cointegrating relationships by the eigenvectors corresponding to the r smallest eigenvalues of an averaged periodogram matrix of tapered, differenced observations. The number of frequencies m used in the periodogram average is held fixed as the sample size grows. We first show that the averaged periodogram matrix converges in…