Anomaly Time Series

In atmospheric sciences and some other applications of statistics, an anomaly time series is the time series of deviations of a quantity from some mean. Similarly a standardized anomaly series contains values of deviations divided by a standard deviation. Location and scale measures that are resistant to the effects of outliers are sometimes used as the basis of the transformation.

The location and scale parameters used in forming an anomaly time-series may either be constant or may themselves be time series. For example, if the original time series consisted of temperatures measured every hour, the effect of typical daily cycles of temperature might be remove by subtracting a time series containing mean temperature values for each hour of the day: clearly, this can be extended by including seasonal variations of temperature.

In the atmospheric sciences, the climatological annual cycle is often used as the mean value. Famous atmospheric anomaly time series are for instance the Southern Oscillation index (SOI) and the North Atlantic oscillation index. SOI is the atmospheric component of El Niño, while NAO plays an important role for European weather by modification of the exit of the Atlantic storm track.