Exploring Irregular Time Series Through Non-Uniform Fast Fourier Transform

Abstract

One of the fundamental shortcoming of the popular analysis tools for time series is that they require the data to be taken at uniform time intervals. However, the real-world time series, such as those from financial markets, are mostly from irregular time intervals. It is a common practice to resample 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 on 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 directly explore the dynamics of irregular time series through a tool 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. Results accurately capture well-known structural features in the trading records, such as weekly and daily cycles, and at the same time also reveal unknown or unexplored features, such as the presence of multiple power laws. In particular, we observe a new power law in the Fourier spectra in recent years.

Keywords: In-homogeneous Time Series, Non-Uniform Fourier Transform, High Frequency Trading, Sampling Frequency, Volume Time

JEL Classification: C02, D52, D53, G14