High-dimensional, nonstationary, and nonlinear spatio-temporal time series commonly seen in practice entails computationally effective and efficient statistical methods to analyze them. The vector error-correction model (VECM) is widely used for modeling unit-root nonstationary time series. To improve VECM’s capability to capture the probable nonlinearity in the data, we propose an empirical nonlinear function to describe VECM’s trend term and name the model Emp-VECM. Implementing Emp-VECM in data analysis requires a robust cointegration test and a spatial dimension-reduction technique. Here we revamp the current cointegration test to be robust against the nonlinear trend in the data. To overcome the curse of dimensionality, we apply Emp-VECM in model fitting to only those time series representing the space-time dynamics of the data. Selecting the representative series is achieved via a two-step spatial clustering and dimension-reduction procedure. Namely, we first cluster the spatial domain of the data by K-means or model-based clustering and then select a small set of empirical dynamic quantile (EDQ) series within each cluster to represent. The performance of this Emp-VECM-EDQ method is assessed by using real-world ground motion data giving \(R^2\approx 0.99\) . Our method is shown to successfully capture the nonlinearity and nonstationarity in high-dimensional spatio-temporal time series analysis.