PhD Public Lecture (DSAS) - Ning Sun

This thesis focuses on discussing non-parametric estimators and their asymptotic behaviors for indices developed to characterize bi-variate time series. There are typically two types of indices depending on whether the distributional information is involved. For the indices containing the distributional information of the bivariate stationary time series, we particularly focus on the index called the tail order of maximal dependence (TOMD), which is an improvement of the tail order. For the indices without distributional information of the bivariate time series, we focus on an anomaly detection index for univariate input-output systems.

This thesis integrates three articles. The first article (Chapter 2) proposes the average block-minima estimator for the TOMD and discusses theoretical aspects of this estimator under the independently identically distribution (i.i.d.) assumption, including asymptotic behavior and bias reduction. The performance of this estimator is justified by simulation studies using Marshall-Olkin copula and generalized Clayton copula, respectively. The second article (Chapter 3) examines the performance of the average block-minima estimator on stationary bi-variate time series using simulation studies. Applications of the estimator on three groups of financial assets are employed to illustrate how the estimation method could be used in practice. The third article (Chapter 4) generalizes an existing anomaly detection index for input-output systems with i.i.d. inputs to those with stationary inputs. Theoretical evidence and illustrative examples are provided to validate the performance of the existing index for systems with stationary inputs.