Fractional Differencing in Discrete Time

Quantitative Finance, 13, 2013.

27 Pages Posted: 27 Jul 2011 Last revised: 10 Feb 2018

See all articles by John Elder

John Elder

Colorado State University

Robert J. Elliott

University of Calgary - Haskayne School of Business; University of Alberta - Department of Mathematical and Statistical Sciences; University of South Australia

Hong Miao

Colorado State University, Fort Collins - Department of Finance & Real Estate

Date Written: July 23, 2011

Abstract

This paper consists of two parts, a theoretical followed by an empirical contribution. We first give a new framework for fractional differencing in discrete time and show how the definition of fractional differencing that is commonly employed in empirical financial applications arises as a special case. We then use these methods to estimate the fractional differencing parameter in the return and volatility for three Comex metal futures contracts. The metal futures are sampled at very high frequencies - five minute intervals over a nearly eight year period.

Keywords: Fractional Difference, Discrete Time, Metal Futures, Long Memory

JEL Classification: C10, J10

Suggested Citation

Elder, John and Elliott, Robert James and Miao, Hong, Fractional Differencing in Discrete Time (July 23, 2011). Quantitative Finance, 13, 2013., Available at SSRN: https://ssrn.com/abstract=1896336 or http://dx.doi.org/10.2139/ssrn.1896336

John Elder

Colorado State University ( email )

Dept of Finance & Real Estate
1272 Campus Delivery
Fort Collins, CO 80523
United States
970-491-2952 (Phone)

HOME PAGE: http://lamar.colostate.edu/~jelder

Robert James Elliott

University of Calgary - Haskayne School of Business ( email )

2500 University Drive, NW
Calgary, Alberta T2N 1N4
Canada

University of Alberta - Department of Mathematical and Statistical Sciences ( email )

Edmonton, Alberta T6G 2G1
Canada
403-492-5811 (Phone)
403-492-6826 (Fax)

University of South Australia ( email )

37-44 North Terrace
Adelaide
Australia

Hong Miao (Contact Author)

Colorado State University, Fort Collins - Department of Finance & Real Estate ( email )

Fort Collins, CO 80523
United States

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