Iterative Algorithm for Time Series Decomposition into Trend and Seasonality: Testing Using the Example of CO(2) Concentrations in the Atmosphere

An iterative algorithm for the decomposition of data series into trend and residual (including the seasonal effect) components is proposed. This algorithm is based on the approaches proposed by the authors in several previous studies and allows unbiased estimates for the trend and seasonal components for data with a strong trend containing different periodic (including seasonal) variations, as well as observational gaps and omissions. The main idea of the algorithm is that both the trend and the seasonal components should be estimated using a signal that is maximally cleaned of any other variations, which are considered a noise. In estimating the trend component, seasonal variation is a noise, and vice versa. The iterative approach allows a priori information to be more completely used in the optimization of models of both trend and seasonal components. The approximation procedure provides maximum flexibility and is fully controllable at all stages of the process. In addition, it allows one to naturally solve the problems in the case of missing observations and defective measurements without filling these dates with artificially simulated values. The algorithm was tested using data on changes in the concentration of CO(2) in the atmosphere at four stations belonging to different latitudinal zones. The choice of these data is explained by the features that complicate the use of other methods, namely, high interannual variability, high-amplitude seasonal variations, and gaps in the series of observed data. This algorithm made it possible to obtain trend estimates (which are of particular importance for studying the characteristics and searching for the causes of global warming) for any time interval, including those that are not multiples of an integer number of years. The rate of increase in the CO(2) content in the atmosphere has also been analyzed. It has been reliably established that in around 2016, the rate of CO(2) accumulation in the atmosphere became stabilized and even tended to decrease. The extent of this stabilization will become clear in the next 2–3 years as new data are available.