Exploring Irregular Time Series through Non-Uniform Fast Fourier Transform

Most popular analysis tools on time series require the data to be taken at uniform time intervals. However, the realworld time series, such as those fromnancial markets, are typically taken at irregular time intervals. It is a common practice to resample or bin the irregular time series into a regular one, but there are significant limitations on this practice. For example, if one is to resample the trading activities of a stock into hourly series, then the time series can only last through the trading day, because there usually is no trading in the night. In this work, we explore the dynamics of irregular time series through a high-performance computing algorithm known as Non-Uniform Fast Fourier Transform (NUFFT).To illustrate its effectiveness, we apply NUFFT on the trading records of natural gas futures contracts for the last seven years. Tests show that NUFFT results accurately capture well-known structural features in the trading records, such as weekly and daily cycles. At the same time the results also reveal unexplored features, such as the presence of multiple power laws. In particular, we observe an emerging power law in the Fourier spectra in recent years. We also detect a strong Fourier component at the precise frequency once per minute, which implies significant automated trading activities might be triggered by clock.