• Bernoulli
  • Volume 23, Number 4A (2017), 2860-2886.

Information criteria for multivariate CARMA processes

Vicky Fasen and Sebastian Kimmig

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Multivariate continuous-time ARMA$(p,q)$ ($\operatorname{MCARMA} (p,q)$) processes are the continuous-time analog of the well-known vector ARMA$(p,q)$ processes. They have attracted interest over the last years. Methods to estimate the parameters of an MCARMA process require an identifiable parametrization such as the Echelon form with a fixed Kronecker index, which is in the one-dimensional case the degree $p$ of the autoregressive polynomial. Thus, the Kronecker index has to be known in advance before parameter estimation can be done. When this is not the case, information criteria can be used to estimate the Kronecker index and the degrees $(p,q)$, respectively. In this paper, we investigate information criteria for MCARMA processes based on quasi maximum likelihood estimation. Therefore, we first derive the asymptotic properties of quasi maximum likelihood estimators for MCARMA processes in a misspecified parameter space. Then, we present necessary and sufficient conditions for information criteria to be strongly and weakly consistent, respectively. In particular, we study the well-known Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) as special cases.

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Bernoulli, Volume 23, Number 4A (2017), 2860-2886.

Received: May 2015
Revised: January 2016
First available in Project Euclid: 9 May 2017

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AIC BIC CARMA process consistency information criteria law of iterated logarithm Kronecker index quasi maximum likelihood estimation


Fasen, Vicky; Kimmig, Sebastian. Information criteria for multivariate CARMA processes. Bernoulli 23 (2017), no. 4A, 2860--2886. doi:10.3150/16-BEJ830.

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