Moving Average Convergence/Divergence analysis of geophysical and geochemical time series: application to the 2011-2012 El Hierro eruption

Financial markets specialists often use multiscale analysis on different kind of time series. Many tools have been developed for these tasks. Two of them, widely used, are: candlestick charts and technical indicators. Our approach consists in using both tools to analyze geophysical and geochemical time series.

In this work we represent signals using candlesticks at user selected time scales. In our case we use four summary quantities of the signal: the amplitude of the first sample, the maximum amplitude within the candle, the minimum amplitude and the amplitude of the last sample used in the candle. We show how the graphical candlestick representation alone is able to emphasize representative changes within the time-series in a multiscale fashion.

On the other hand, many technical indicators have been defined to extract further information from such type of charts. Among the most commonly used technical indicators are: Simple Moving Average (SMA), Exponential Moving Average (EMA) and Moving Average Convergence/Divergence (MACD). EMA is a temporal smoothing with an exponential weighting determined by a time scale factor. MACD is the difference between EMA realized at a short scale with another EMA at a larger scale. For instance, a commonly used MACD in financial markets is computed using scales of 12 and 26 days. In the case of actual geophysical and geochemical datasets, such scales should be selected on the basis of the time scales of interest.

Using tests realized on synthetic datasets we demonstrate that MACD is a proxy for the derivative of time-series, event with a very high noise level. This is of course of great interest when analyzing geophysical and geochemical time series, with the aim of detecting changes in their trends. We applied candlestick analysis to various seismological and geochemical datasets, in particular we show an example application to recent 2011-2012 eruption of the island of El Hierro in the Canary Islands, highlighting the capability of this method to detect changes in the trend of time-series earlier and better that other simpler techniques.