2020/09/09 by Carlos Velasco, Carlos A. Velasco, Velasco, Carlos
Computer Science · Mathematics · #62M10 #62M15 #Advanced Statistical Methods and Models #Blind Source Separation Techniques #FOS: Mathematics #Statistical and numerical algorithms #Statistics Theory (math.ST) #math.ST #msc:62M10 #msc:62M15 #stat.TH
paper · pdf · doi:10.48550/arxiv.2009.04428
71 pages, 1 figure
arxiv created 2020/09/09 · openalex publication_date 2020/09/09 · arxiv updated 2020/09/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly non-fundamental or non-causal, through a frequency domain criterion based on a new representation of the higher order spectral density arrays of vector linear processes. This allows to identify the location of the roots of the determinantal lag matrix polynomials based on higher order cumulants dynamics and to identify the rotation of the model errors leading to the structural shocks up to sign and permutation. We describe sufficient conditions for global and local parameter identification that rely on simple rank assumptions on the linear dynamics and on finite order serial and component independence conditions for the structural innovations. We generalize previous univariate analysis to develop asymptotically normal and efficient estimates exploiting second and non-Gaussian higher order dynamics given a particular structural shocks ordering without assumptions on causality or invertibility. Bootstrap approximations to finite sample distributions and the properties of numerical methods are explored with real and simulated data.