ITERATIVE ALGORITHM FOR TIME SERIES DECOMPOSITION INTO TREND
AND SEASONALITY AND ITS TESTING ON CO₂ CONCENTRATION
IN THE ATMOSPHERE AS AN EXAMPLE

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

* e-mail: al_sidorin@hotmail.com

Abstract. An iterative algorithm for 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 works, and allows the researcher to obtain non-biased estimates of the trend and seasonal components for data with a strong trend, containing various periodic variations, including seasonal, as well as gaps and missing observations. The main idea of the algorithm is that both the trend and the seasonal components should be estimated using the signal that is maximally cleaned of any other variations that are considered as interference, when assessing the trend component, seasonal variation is a hindrance, and vice versa. The iterative approach allows the researcher to be naturally included in the optimization procedure for 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 you to naturally solve the problems that arise in the presence of missed observations and defective measurements, without filling such dates with artificially simulated values. The algorithm was tested on the example of data on changes in the concentration of CO₂ in the atmosphere at 4 stations belonging to different latitudinal zones. The choice of these data for testing the algorithm is due to the presence of features that complicate the use of other methods, namely: high interannual variability, the presence of high-amplitude seasonal variations, as well as gaps in the series of observed data. The application of the described algorithm made it possible to carry out trend assessments (which are of particular importance for studying the characteristics and searching for the causes of global warming) for any time intervals, including non-multiples of an integer number of years, etc. The rate of increase in the CO2 content in the atmosphere was also analyzed. It has been reliably established that approximately in 2016, the rate of CO₂ accumulation in the atmosphere stabilized and even tends to decrease. How stable this trend is will become clear in the next 2–3 years as new data accumulates.

Keywords: time series, time series analysis, time series decomposition, iterative algorithm, trend, periodic components, seasonal periodicity, algorithm testing, CO₂ concentration in the atmosphere.

About the authors

DESHCHEREVSKII Aleksey Vladimirovich – Schmidt Institute of Physics of the Earth, Russian Academy of Sciences. Russia, 123242, Moscow, Bolshaya Gruzinskaya st., 10-1. E-mail: adeshere@ifz.ru

SIDORIN Alexander Yakovlevich – Schmidt Institute of Physics of the Earth, Russian Academy of Sciences. Russia, 123242, Moscow, Bolshaya Gruzinskaya st., 10-1. E-mail: al_sidorin@hotmail.com

Cite this article as: Deshcherevskii A.V., Sidorin A.Ya. Iterative algorithm for time series decomposition into trend and seasonality and its testing on CO₂ concentration in the atmosphere as an example, Geofizicheskie Protsessy i Biosfera (Geophysical Processes and Biosphere), 2021, vol. 20, no. 1, pp. 128–151 (in Russian). https://doi.org/10.21455/gpb2021.1-11

English version: Izvestiya, Atmospheric and Oceanic Physics, 2021, vol. 57, iss. 7. ISSN: 0001-4338 (Print), 1555-628X (Online). https://link.springer.com/journal/volumesAndIssues/11485