Chiang Mai Journal of Science

     Dynamic Mode Decomposition (DMD) with time delay embedding is used to predict dynamic patterns in univariate time series. An important pattern that can be extracted using DMD is the trend or global change in a time series which is useful for producing reliable forecast. DMD utilizes the computationally efficient singular value decomposition (SVD) to produce a low rank approximation of the linear operator that brings about the dynamic patterns in the time series. Trend in the time series is translated as dynamic modes of the operator with low frequencies. The time evolution of this low frequency pattern produces forecast of the time series. In this paper, we outline the strategies for extracting trend component from COVID-19 time series of Malaysia. It is discovered that, other than identifying modes with slow varying frequencies, we need to also resolve the time stamp delay, so that mean-square error of the reconstructed time series is minimal. Information of the magnitude and phase of DMD modes are useful to identify persistent patterns and remove nonstationary ones. We compare the performance of DMD with another SVD-based method which is the singular spectrum analysis (SSA) and our results highlight certain fundamental difference between these two methods. The forecasts from SSA tend to lean towards the direction of maximum variance, producing low reconstruction error but slow to detect sudden changes in the time series. On the other hand, forecasts from DMD captures the phases of dominant modes that dictates the overall global pattern, hence providing a better prediction of future dynamics of the time series.