Deep spectral copula mechanisms modeling coupled and volatile multivariate time series

Exploring inter- and intra-time series relations and handling volatile covariates form various challenges in modeling Coupled and Volatile Multivariate Time Series (CVMTS). A typical CVMTS data is the COVID-19 case time series across multiple countries, whose covariates may involve high volatility caused by missing samples. The existing approaches merely focus on a single set of multivariate time series or multiple multivariate time series without considering their volatile temporal covariates. They do not sufficiently characterize CVMTS features by explicitly modeling intra- and inter-MTS couplings and effectively handling volatile covariates in multiple multivariate time series. Accordingly, we propose Deep Spectral Copula Mechanisms (DSCM) to adapt CVMTS. Specifically, DSCM (1) incorporates a Singular Spectral Analysis (SSA) module to reduce the volatility of multiple covariates; (2) applies an intra-MTS coupling module to explicitly model the temporal couplings within a single set of multivariate time series; and (3) transforms target variables into joint probability distributions by Gaussian copula transformation to establish inter-MTS couplings across multiple multivariate time series. Substantial experiments on COVID-19 time-series data from multiple countries indicate the superiority of DSCM over state-of-the-art approaches.