On fully indecomposable matrices

Fenner, Trevor; Loizou, G.

doi:10.1016/s0022-0000(71)80018-1

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…The result follow from the fact that the non zero elements of W k are the same of (W k W k ) (W k W k ) and consequently of W k W k . Then, since the multiplication of two fully indecomposable matrices is fully indecomposable, and fully indecomposability implies irreducibility, Fenner and Loizou (1971), under the hypothesis of the lemma there is a at least one k = 1 . .…”

Section: B12 Proof Of Lemma 1 On Page 13mentioning

confidence: 97%

Networks in risk spillovers: A multivariate GARCH perspective

Billio

Caporin

Frattarolo

et al. 2023

Econometrics and Statistics

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We propose a spatiotemporal approach for modeling risk spillovers using time-varying proximity matrices based on observable financial networks and introduce a new bilateral specification. We study covariance stationarity and identification of the model, and analyze consistency and asymptotic normality of the quasi-maximum-likelihood estimator. We show how to isolate risk channels and we discuss how to compute target exposure able to reduce system variance. An empirical analysis on Euro-area cross-country holdings shows that Italy and Ireland are key players in spreading risk, France and Portugal are the major risk receivers, and we uncover Spain's non-trivial role as risk middleman.

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Section: B12 Proof Of Lemma 1 On Page 13mentioning

confidence: 97%

Networks in risk spillovers: A multivariate GARCH perspective

Billio

Caporin

Frattarolo

et al. 2023

Econometrics and Statistics

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Combinatorial aspects of rectangular non-negative matrices

Fenner

Loizou

1977

Discrete Mathematics

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Stochastic forms of non-negative matrices and Perron-regularity

Gómez

2016

ELA

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Abstract. Given a real non-negative square matrix A, the problem of determining when two distinct constructions of stochastic matrices associated to A coincide is studied. All the constructions (or stochastic forms) that are considered are diagonal forms, i.e., the transformations act like A → αD (r) AD (c) , where D (r) and D (c) are diagonal matrices with positive diagonals and α > 0, all depending on A.

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On fully indecomposable matrices

Cited by 3 publications

References 17 publications

Networks in risk spillovers: A multivariate GARCH perspective

Networks in risk spillovers: A multivariate GARCH perspective

Combinatorial aspects of rectangular non-negative matrices

Stochastic forms of non-negative matrices and Perron-regularity

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