کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10524511 | 957563 | 2005 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Factorization of moving-average spectral densities by state-space representations and stacking
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز عددی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Factorization of moving-average spectral densities by state-space representations and stacking Factorization of moving-average spectral densities by state-space representations and stacking](/preview/png/10524511.png)
چکیده انگلیسی
To factorize a spectral density matrix of a vector moving average process, we propose a state space representation. Although this state space is not necessarily of minimal dimension, its associated system matrices are simple and most matrix multiplications involved are nothing but index shifting. This greatly reduces the complexity of computation. Moreover, in this article we stack every q consecutive observations of the original process MA(q) and generate a vector MA(1) process. We consider a similar state space representation for the stacked process. Consequently, the solution hinges on a surprisingly compact discrete algebraic Riccati equation (DARE), which involves only one Toeplitz and one Hankel block matrix composed of autocovariance functions. One solution to this equation is given by the so-called iterative projection algorithm. Each iteration of the stacked version is equivalent to q iterations of the unstacked one. We show that the convergence behavior of the iterative projection algorithm is characterized by the decreasing rate of the partial correlation coefficients for the stacked process. In fact, the calculation of the partial correlation coefficients via the Whittle algorithm, which takes a very simple form in this case, offers another solution to the problem. To achieve computational efficiency, we apply the general Newton procedure given by Lancaster and Rodman to the DARE and obtain an algorithm of quadratic convergence rate. One immediate application of the new algorithms is polynomial stabilization. We also discuss various issues such as check of positivity and numerical implementation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 96, Issue 2, October 2005, Pages 425-438
Journal: Journal of Multivariate Analysis - Volume 96, Issue 2, October 2005, Pages 425-438
نویسندگان
Lei M. Li,