Online Correlation Change Detection for Large-Dimensional Data with An Application to Forecasting of El Ni\~no Events

We consider detecting change points in the correlation structure of streaming large-dimensional data with minimum assumptions posed on the underlying data distribution. Depending on the $\ell_1$ and $\ell_{\infty}$ norms of the squared difference of vectorized pre-change and post-change correlation matrices, detection statistics are constructed for dense and sparse settings, respectively. The proposed detection procedures possess the bless-dimension property, as a novel algorithm for threshold selection is designed based on sign-flip permutation. Theoretical evaluations of the proposed methods are conducted in terms of average run length and expected detection delay. Numerical studies are conducted to examine the finite sample performances of the proposed methods. Our methods are effective because the average detection delays have slopes similar to that of the optimal exact CUSUM test. Moreover, a combined $\ell_1$ and $\ell_{\infty}$ norm approach is proposed and has expected performance for transitions from sparse to dense settings. Our method is applied to forecast El Ni{\~n}o events and achieves state-of-the-art hit rates greater than 0.86, while false alarm rates are 0. This application illustrates the efficiency and effectiveness of our proposed methodology in detecting fundamental changes with minimal delay.