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Estimation of causal continuous‐time autoregressive moving average random fields

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  • Claudia Klüppelberg
  • Viet Son Pham

Abstract

We estimate model parameters of Lévy‐driven causal continuous‐time autoregressive moving average 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.

Suggested Citation

  • Claudia Klüppelberg & Viet Son Pham, 2021. "Estimation of causal continuous‐time autoregressive moving average random fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 132-163, March.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:1:p:132-163
    DOI: 10.1111/sjos.12444
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    References listed on IDEAS

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    1. Peter J. Brockwell & Yasumasa Matsuda, 2017. "Continuous auto-regressive moving average random fields on ℝ-super-n," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 833-857, June.
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    4. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    5. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
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