Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Portmanteau Tests for ARMA Models with Infinite Variance   Autoregressive and moving-average (ARMA) models with stable Paretian errors
is one of the most studied models for time series with infinite variance.
Estimation methods for these models have been studied by many researchers but
the problem of diagnostic checking fitted models has not been addressed. In
this paper, we develop portmanteau tests for checking randomness of a time
series with infinite variance and as a diagnostic tool for checking model
adequacy of fitted ARMA models. It is assumed that least-squares or an
asymptotically equivalent estimation method, such as Gaussian maximum
likelihood in the case of AR models, is used. And it is assumed that the
distribution of the innovations is IID stable Paretian. It is seen via
simulation that the proposed portmanteau tests do not converge well to the
corresponding limiting distributions for practical series length so a
Monte-Carlo test is suggested. Simulation experiments show that the proposed
test procedure works effectively. Two illustrative applications to actual data
are provided to demonstrate that an incorrect conclusion may result if the
usual portmanteau test based on the finite variance assumption is used.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex