Unified Methodology for Detecting Trend Changes and Outliers in Time Series: application to Ground Deformation in the Virunga Volcanic Province.

Abstract:

Detecting trend changes and outliers are common needs in applied time series analysis. Here we propose a tool combining various robust methods to perform simultaneously these two tasks. Such a unified tool is well adapted to the analysis of extensive databases. We use it to analyze ground deformations associated to volcanic activity in the Virunga Volcanic Province. Trend changes are estimated using weighted moving average filter, locally weighted scatterplot smoothers and smoothing splines. Significance of detected trend changes is estimated using parametric and non-parametric statistical tests such as Mann-Kendall, Spearmans Rho and Pearson correlation methods. Outliers are detected using both standardized residuals from best-fit model and Chebyshev’s inequality. On one side observations that have a studentized residual outside the ± 2 range are considered statistically significant at the 95% a level and potential outliers. On the other hand Chebyshev’s inequality gives a bound of what percentage of the data falls outside of k standard deviations from the mean calculating upper and lower outlier detection limits. When multiple components of displacements are available (such as vertical, North-South and East-West GPS time series), the outliers detection is performed on each component separately, then jointly. The effectiveness of the tool is demonstrated by analyzing 5 years of data recorded by the permanent GNSS volcano monitoring network in Goma as well as the extensive amount of MSBAS Multidimensional InSAR time series (Samsonov and dOreye, 2012) recorded in the Virunga during 2003-2013 time period.