Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions

Journal article

Fabian Mies, Ansgar Steland
Bernoulli, vol. 29(4), 2023, pp. 3114-3140

arXiv

Cite

APA Click to copy
Mies, F., & Steland, A. (2023). Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions. Bernoulli, 29(4), 3114–3140. https://doi.org/10.3150/22-BEJ1577

Chicago/Turabian Click to copy
Mies, Fabian, and Ansgar Steland. “Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions.” Bernoulli 29, no. 4 (2023): 3114–3140.

MLA Click to copy
Mies, Fabian, and Ansgar Steland. “Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions.” Bernoulli, vol. 29, no. 4, 2023, pp. 3114–40, doi:10.3150/22-BEJ1577.

BibTeX Click to copy

@article{mies2023a,
  title = {Sequential Gaussian Approximation for Nonstationary Time Series in High Dimensions},
  year = {2023},
  issue = {4},
  journal = {Bernoulli},
  pages = {3114-3140},
  volume = {29},
  doi = {10.3150/22-BEJ1577},
  author = {Mies, Fabian and Steland, Ansgar}
}

Gaussian couplings of partial sum processes are derived for the high-dimensional regime d=o(n1/3). The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities depend explicitly on the dimension and on a measure of nonstationarity, and are thus also applicable to arrays of random vectors. To enable high-dimensional statistical inference, a feasible Gaussian approximation scheme is proposed. Applications to sequential testing and change-point detection are described.