Controlling non-stationarity and periodicities in time series generation using conditional invertible neural networks

Generated synthetic time series aim to be both realistic by mirroring the characteristics of real-world time series and useful by including characteristics that are useful for subsequent applications, such as forecasting and missing value imputation. To generate such realistic and useful time series, we require generation methods capable of controlling the non-stationarity and periodicities of the generated time series. However, existing approaches do not consider such explicit control. Therefore, in the present paper, we present a novel approach to control non-stationarity and periodicities with calendar and statistical information when generating time series. We first define the requirements for methods to generate time series with non-stationarity and periodicities, which we show are not fulfilled by existing generation methods. Second, we formally describe the novel approach for controlling non-stationarity and periodicities in generated time series. Thirdly, we introduce an exemplary implementation of this approach using a conditional Invertible Neural Network (cINN). We evaluate this cINN empirically in experiments with real-world data sets and compare it to state-of-the-art time series generation methods. Our experiments show that the evaluated cINN can generate time series with controlled periodicities and non-stationarity, and it also generally outperforms the selected benchmarks.