Abstract
High-dimensional, non-stationary vector time-series data are often seen in ground motion monitoring of geo-hazard events, e.g., landslides. For timely and reliable forecasts from such data, we developed a new statistical approach based on two advanced econometric methods, i.e., error-correction cointegration (ECC) and vector autoregression (VAR), and a newly developed dimension reduction technique named empirical dynamic quantiles (EDQ). Our ECC–VAR–EDQ method was born by analyzing a big landslide dataset, comprising interferometric synthetic-aperture radar (InSAR) measurements of ground displacement that were observed at 5090 time states and 1803 locations on a slope. The aim was to develop an early warning system for reliably forecasting any impending slope failure whenever a precursory slope deformation is on the horizon. Specifically, we first reduced the spatial dimension of the observed landslide data by representing them as a small set of EDQ series with negligible loss of information. We then used the ECC–VAR model to optimally fit these EDQ series, from which forecasts of future ground motion can be efficiently computed. Moreover, our method is able to assess the future landslide risk by computing the relevant probability of ground motion to exceed a red-alert threshold level at each future time state and location. Applying the ECC–VAR–EDQ method to the motivating landslide data gives a prediction of the incoming slope failure more than 8 days in advance.
Highlights
Behaviors of the geological processes underpinning such geo-hazard events are mostly complicated in both space and time, in that the multivariate time series data collected from monitoring these processes by modern techniques, such as interferometric synthetic-aperture radar (InSAR), are often high-dimensional and non-stationary
Using error-correction cointegration (ECC) and vector autoregression (VAR) to analyze non-stationary vector time series can be computationally infeasible if the vector dimensionality is too high, e.g., k = 1803 for the landslide data, because the number of unknown parameters involving statistical inference will be of order
We have developed an ECC–VAR–empirical dynamic quantiles (EDQ) method to characterize and analyze highdimensional, unit-root non-stationary vector time series
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. There exist few statistical methods capable of analyzing high-dimensional non-stationary InSAR time series for timely and reliable forecasts of geo-hazard events [3]. We resort to searching for certain linear transformation of the data consisting of lagged time-difference operations, by which the non-stationary landslide time series can be converted to be stationary before applying the stationary VAR methodology The technique underpinning such linear transformation is the so-called error-correction cointegration (ECC) method; cf Chapter 5 in [5]. Using ECC and VAR to analyze non-stationary vector time series can be computationally infeasible if the vector dimensionality is too high, e.g., k = 1803 for the landslide data, because the number of unknown parameters involving statistical inference will be of order.
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