Likelihood asymptotics of stationary Gaussian arrays

Preprint

Carsten H. Chong, Fabian Mies
arXiv, 2502.09229, 2025

DOI: 10.2139/ssrn.5069904

arXiv SSRN

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APA Click to copy
Chong, C. H., & Mies, F. (2025). Likelihood asymptotics of stationary Gaussian arrays. ArXiv, 2502.09229. https://doi.org/10.2139/ssrn.5069904

Chicago/Turabian Click to copy
Chong, Carsten H., and Fabian Mies. “Likelihood Asymptotics of Stationary Gaussian Arrays.” arXiv 2502.09229 (2025).

MLA Click to copy
Chong, Carsten H., and Fabian Mies. “Likelihood Asymptotics of Stationary Gaussian Arrays.” ArXiv, vol. 2502.09229, 2025, doi:10.2139/ssrn.5069904 .

BibTeX Click to copy

@article{carsten2025a,
  title = {Likelihood asymptotics of stationary Gaussian arrays},
  year = {2025},
  journal = {arXiv},
  volume = {2502.09229},
  doi = {10.2139/ssrn.5069904 },
  author = {Chong, Carsten H. and Mies, Fabian}
}

This paper develops the asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models to be locally asymptotically normal in Le Cam's sense, which in particular implies the asymptotic efficiency of the maximum likelihood estimator. Unique features of the array setting covered by our theory include potentially non-diagonal rate matrices as well as spectral densities that satisfy different power-law bounds at different frequencies and may fail to be uniformly integrable. To illustrate our theory, we study efficient estimation for noisy fractional Brownian motion under infill asymptotics and for a class of autoregressive models with moderate deviations from a unit root.

Keywords: Fractional Brownian motion, High-frequency data, Local asymptotic normality, Local-to-unity model, Maximum likelihood estimator, Mildly integrated process, Toeplitz matrix

Rates of convergence for the AR(1) parameter a, in different local-to-unity regimes.