Dynamic Mode Decomposition for Univariate Time Series: Analysing Trends and Forecasting

Santosh Tirunagari (1) , Samaneh Kouchaki (2) , Norman Poh (1) , Miroslaw Bober (1) , David Windridge (3)

1 Faculty of Engineering & Physical Sciences
2 Department of Evolutionary and Genomic Sciences
3 Department of Computer Science

This study introduces the method of Dynamic Mode Decomposition (DMD) for analysing univariate time series by forecasting as well as extracting trends and frequencies. The key advantage of DMD is its data-driven nature which does not rely on any prior assumptions (like Singular Spectrum Analysis (SSA)) except the inherent dynamics which are captured over time. Indeed, this study will show that the DMD eigenvalues with frequencies that are closer to the origin in the complex plane capture the trends in the time series. Moreover, the temporal evolution of the DMD modes, which is preserved via the Vandermonde matrix, can be used to reconstruct the desired components and perform forecasting at the same time. The results at various noise levels on simulated data suggests that DMD is a promising approach to modelling a time series with a noisy structure. Although these properties are not new in the DMD literature, the novel contributions of this paper are in making the method of DMD work for univariate time series through a four staged pipeline. Thus, this is the first work that shows DMD can be used for modelling, predicting, and forecasting a univariate time series.

Mots clés: Univariate Time series modelling; DMD; forecast; prediction; trends; noise; Dynamic Mode Decomposition

Domaines: Informatique [cs]

Santosh Tirunagari, Samaneh Kouchaki, Norman Poh, Miroslaw Bober, David Windridge. Dynamic Mode Decomposition for Univariate Time Series: Analysing Trends and Forecasting. 2017. ⟨hal-01463744⟩