Modelling High-Dimensional Time Series with Nonlinear and Nonstationary Phenomena for Landslide Early Warning and Forecasting †

Abstract

Landslides are nonstationary and nonlinear phenomena, which are often recorded as high-dimensional vector time series manifesting spatiotemporal dependence. Contemporary econometric methods use error-correction cointegration (ECC) and vector autoregression (VAR) to handle the nonstationarity but ignore the nonlinear trend. Here, we improve the ECC-VAR methodology by inserting a nonlinear trend (Formula presented.) into the model and nonparametrically estimating it by penalised maximum likelihood, and name this method ECC-VAR- (Formula presented.). Assisted by the empirical dynamic quantiles (EDQ) dimension reduction technique, it is sufficient to apply ECC-VAR- (Formula presented.) to just a small number of representative EDQ series to surmise the whole dataset. The application of this ECC-VAR- (Formula presented.) is well fitted to the real-world slope dataset ((Formula presented.)) that consists of 1803 time series, each having 5090 time states. In addition to the forecast values, we also provide three risk assessments to predict locations, time and risk of a future failure with quantified uncertainty for building an early-warning system (e.g., predicted time of failure (ToF), where the minimum error is 2.7 h before the actual ToF).