Doctoral thesis
Open access

Contributions to time series analysis

ContributorsXu, Haotian
Defense date2021-06-29

This thesis consists of two parts. In the first part, we focus on parametric modeling, estimation and statistical inference of multivariate time series. We put forward a new multivariate modeling and estimation approach allowing to characterize and estimate complex latent dependence structures in a computationally efficient manner with respect to existing approaches. This approach is applied, in particular, to inertial sensor calibration. The statistical properties of this approach allows, in particular, to test dependence between sensors, to integrate their dependence within the navigation filter and to construct an optimal virtual sensor that can be used to improve navigation accuracy. In the second part, we focus on autocovariance estimation of high-dimensional time series, where the sample autocovariance matrix perform inappropriately. We propose and study two groups of robust estimation methods for autocovariance matrices of a high-dimensional heavy-tailed stationary time series. These proposed methods are shown to achieve optimal error bounds with respect to matrix max-norm and matrix spectral-norm respectively. Our non-asymptotic results are based on concentration inequalities under dependence and allow to clarify the impact of high-dimensionality, heavy-tailedness and temporal dependence on various estimation procedures. We also provide several applications of our results in time series analysis, including the long-run covariance matrix estimation, the autocorrolation matrix estimation and the $l_{infty}$-type Gaussian approximation for high-dimensional vector. The finite sample performance of our estimators are also justified by Monte Carlo simulations.

  • Gaussian approximation
  • Heavy-tail
  • High-dimension
  • Robust statistics
  • Signal processing
  • Time series
  • Wavelet variance
Citation (ISO format)
XU, Haotian. Contributions to time series analysis. 2021. doi: 10.13097/archive-ouverte/unige:152920
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Creation06/30/2021 4:07:00 PM
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