Each week, we select a recently published Open Access article to feature. This week’s article comes from the Scandinavian Journal of Statistics and considers estimation of causal continuous‐time autoregressive moving average random fields.
The article’s abstract is given below, with the full article available to read here.
Estimation of causal continuous‐time autoregressive moving average random fields. Scand J Statist. 2020; 1– 32. https://doi.org/10.1111/sjos.12444, .
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.