Stochastic models decompose (filter) the dynamics of time series into deterministic and random components. From the deterministic component we can make predictions of future steps. Finding a suitable stochastic model thus solves the problem of forecasting in some cases. For highly non-linear systems or high dimensional input variables, it is more promising to use a machine learning model instead of an analytical model, like neural networks with LSTM layers or simpler approaches to be able to resolve the interactions and non-linearities.

In various projects we worked on predicting the seasonal cycle of temperature, air pollution, and animal movements with different approaches, suitable for the respective data.

Directedeness, correlations, and daily cycles in springbok motion: from data over stochastic models to movement prediction
PG Meyer, AG Cherstvy, H Seckler, R Hering, N Blaum, F Jeltsch & R Metzler (2023) Phys. Rev. Research 5, 043129.

Characterizing variability and predictability for air pollutants with stochastic models
PG Meyer, H Kantz & Y Zhou (2021). Chaos, 31(3), 033148.

Spring onset forecast using harmonic analysis on daily mean temperature in Germany
Q Deng, PG Meyer, Z Fu & H Kantz (2020). Environmental Research Letters, 15(10), 104069.