Exploring Irregular Time Series Through Non-Uniform Fast Fourier Transform

Proceedings of the International Conference for High Performance Computating, IEEE, 2014.

26 Pages Posted: 30 Aug 2014 Last revised: 5 Mar 2016

See all articles by Jung Heon Song

Jung Heon Song

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab)

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; AQR Capital Management, LLC

Horst Simon

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab)

Kesheng Wu

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab)

Date Written: August 26, 2014

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

Suggested Citation

Song, Jung Heon and López de Prado, Marcos and Simon, Horst and Wu, Kesheng, Exploring Irregular Time Series Through Non-Uniform Fast Fourier Transform (August 26, 2014). Proceedings of the International Conference for High Performance Computating, IEEE, 2014.. Available at SSRN: https://ssrn.com/abstract=2487656 or http://dx.doi.org/10.2139/ssrn.2487656

Jung Heon Song (Contact Author)

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab) ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

Marcos López de Prado

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

AQR Capital Management, LLC

One Greenwich Plaza
Greenwich, CT 06830
United States

HOME PAGE: http://www.aqr.com

Horst Simon

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab) ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

Kesheng Wu

University of California, Berkeley - Lawrence Berkeley National Laboratory (Berkeley Lab) ( email )

1 Cyclotron Road
Berkeley, CA 94720
United States

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