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 c(t) into the model and nonparametrically estimating it by penalised maximum likelihood, and name this method ECC-VAR-c(t). Assisted by the empirical dynamic quantiles (EDQ) dimension reduction technique, it is sufficient to apply ECC-VAR-c(t) to just a small number of representative EDQ series to surmise the whole dataset. The application of this ECC-VAR-c(t) is well fitted to the real-world slope dataset (R2=0.99) 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).

Keywords

• vector time series
• nonlinear and nonstationary
• error-correction cointegration
• dimension reduction