Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Convergence of Finite Order Approximations of Stationary Time
  Series   The approximation of a stationary time-series by finite order autoregressive
(AR) and moving averages (MA) is a problem that occurs in many applications. In
this paper we study asymptotic behavior of the spectral density of finite order
approximations of wide sense stationary time series. It is shown that when the
on the spectral density is non-vanishing in $[-\pi,\pi]$ and the covariance is
summable, the spectral density of the approximating autoregressive sequence
converges at the origin. Under additional mild conditions on the coefficients
of the Wold decomposition it is also shown that the spectral densities of both
moving average and autoregressive approximations converge in $L_2$ as the order
of approximation increases.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con