Multivariate Carma Random Fields

This paper conducts a multivariate extension of isotropic Levy- driven CARMA random fileds on Rd proposed by Brockwell and Matsuda (2017). Univariate CARMA models are defined as moving averages of a Levy sheet with CARMA kernels defined by AR and MA polynomials. We define multivariate CARMA models by a multivariate extension of CARMA kernels with matrix valued AR and MA polynomials. For the multivariate CARMA models, we derive the spectral density functions as explicit parametric func- tions. Given multivariate irregularly spaced data on R2, we propose Whittle estimation of CARMA parameters to minimize Whittle likelihood given with periodogram matrices and clarify conditions under which consistency and as- ymptotic normality hold under the so called mixed asymptotics. We nally in- troduce a method to conduct kriging for irregularly spaced data on R2 by mul- tivariate CARMA random fields with the estimated parameters in a Bayesian way and demonstrate the empirical properties by tri-variate spatial dataset of simulation and of US precipitation data.