Information Criteria for Multivariate CARMA Processes
| Autor: | Sebastian Kimmig, Vicky Fasen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Information Criteria 01 natural sciences 010104 statistics & probability symbols.namesake Kronecker index Bayesian information criterion Kronecker delta AIC FOS: Mathematics BIC Applied mathematics Statistics::Methodology 0101 mathematics information criteria Mathematics quasi maximum likelihood estimation 62B10 62F12 62M86 (Primary) 62F10 62M10 (Secondary) CARMA process consistency Estimation theory Probability (math.PR) 010102 general mathematics Estimator Autoregressive model symbols Akaike information criterion law of iterated logarithm Row echelon form Mathematics - Probability |
| Zdroj: | Bernoulli 23, no. 4A (2017), 2860-2886 |
| Popis: | Multivariate continuous-time ARMA(p,q) (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 the parameter estimation is 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. 32 pages |
| Databáze: | OpenAIRE |
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