Estimation of causal CARMA random fields

• Main Authors: Klüppelberg, Claudia, Pham, Viet Son
• Format: Journal Article
• Language: English
• Published: 13-02-2019
• Subjects: Mathematics - Statistics Theory; Statistics - Theory
• DOI: 10.48550/arxiv.1902.04962

We estimate model parameters of L\'evy-driven causal CARMA random fields by
fitting the empirical variogram to the theoretical counterpart using a weighted
least squares (WLS) approach. Subsequent to deriving asymptotic results for the
variogram estimator, we show strong consistency and asymptotic normality of the
parameter estimator. Furthermore, we conduct a simulation study to assess the
quality of the WLS estimator for finite samples. For the simulation we utilize
numerical approximation schemes based on truncation and discretization of
stochastic integrals and we analyze the associated simulation errors in detail.
Finally, we apply our results to real data of the cosmic microwave background.