Paul Hill, Juliet Biggs, Victor Ponce Lopez, David Bull

Time series of displacement are now routinely available from satellite InSAR and are used for flagging anomalous ground motion, but not yet for forecasting. Here we test the capabilities of conventional time series analysis and forecasting methods such as SARIMA and supervised machine learning approaches such as Long Short Term Memory (LSTM) in comparison to simple function extrapolation methods. For our initial tests, we focus on forecasting periodic signals and begin by characterising the time-series using sinusoid fitting, seasonal decomposition and autocorrelation functions. We find that the three measures are broadly comparable but identify different types of seasonal characteristic. We use this to select a set of 310 points with highly seasonal characteristics and test the three chosen forecasting methods over prediction windows of 1-9 months. The lowest overall RMSE values are obtained for SARIMA when considering short term predictions ($<$1 month), whereas sinusoid extrapolation performs best for longer predictions ($>$6 months). Machine learning methods (LSTM) perform less well, as is often the case for non-stationary signals. We then test the prediction methods on 2000 randomly selected points with a range of seasonalities and find that simple extrapolation of a constant function performed better overall than any of the more sophisticated time series prediction methods. Comparisons between seasonality and RMSE show a statistically significant improvement in performance with increasing seasonality. This proof-of-concept study demonstrates the potential of time-series prediction for InSAR data but also highlights the limitations of applying these techniques to non-periodic signals or individual measurements points. We anticipate future developments, especially to shorter timescales, will have a broad range of potential applications, from infrastructure stability to volcanic eruptions.