Likelihood asymptotics of stationary Gaussian arrays


Journal article


Carsten H. Chong, Fabian Mies
SSRN preprint, 2024

DOI: 10.2139/ssrn.5069904

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APA   Click to copy
Chong, C. H., & Mies, F. (2024). Likelihood asymptotics of stationary Gaussian arrays. SSRN Preprint. https://doi.org/10.2139/ssrn.5069904


Chicago/Turabian   Click to copy
Chong, Carsten H., and Fabian Mies. “Likelihood Asymptotics of Stationary Gaussian Arrays.” SSRN preprint (2024).


MLA   Click to copy
Chong, Carsten H., and Fabian Mies. “Likelihood Asymptotics of Stationary Gaussian Arrays.” SSRN Preprint, 2024, doi:10.2139/ssrn.5069904 .


BibTeX   Click to copy

@article{carsten2024a,
  title = {Likelihood asymptotics of stationary Gaussian arrays},
  year = {2024},
  journal = {SSRN preprint},
  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.

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