A Test of the Long Memory Hypothesis Based on Self-Similarity

Abstract

A test of the long memory hypothesis based on self-similarityDavidson, James; Rambaccussing, Dooruj Davidson, J., & Rambaccussing, D. (2015). A test of the long memory hypothesis based on self-similarity. Journal of Time Series Econometrics, 7(2), 115-141. [7]. DOI: 10.1515DOI: 10. /jtse-2013 General rights Copyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain.• You may freely distribute the URL identifying the publication in the public portal. Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract: This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skipsampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of significance of the long memory parameter, and a composite test procedure is described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependentsample bootstrap technique to approximate short-run dependence following fractional differencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.

True versus Spurious Long Memory in Cryptocurrencies

“…In this paper, we have contributed to the growing literature on the long memory in cryptocurrencies. We tested for the existence of long memory in the price process by using two novel and superior tests-the log-periodogram bias test of Davidson and Sibbertsen (2009) and the skip-sampling test of Davidson and Rambaccussing (2015)-in addition to the standard GPH and local Whittle procedures. Empirical tests report that long memory exists only in Ethereum returns.…”

“…Such an approach would present a good compromise between size and power. To optimize the trade-off, we applied the log-periodogram test of Davidson and Sibbertsen (2009) and the skip-sampling test of Davidson and Rambaccussing (2015). They test for the null hypothesis of long memory.…”

“…Frequency domain models tend to be nonparametric (or semiparametric) such as the GPH (Geweke and Porter-Hudak 1983), Local Whittle (Robinson 1995), and Fourier (Moulines and Soulier 1999) approaches. Our contribution in this paper is testing for long memory using two novel and superior tests: the log periodogram bias test (Davidson and Sibbertsen 2009) and the skip-sampling test (Davidson and Rambaccussing 2015).…”

A multivariate test against spurious long memory

“…Ohanissian et al (2008) use this property to test for true long memory by testing the equality of ds estimated from different aggregation levels of the same process. A similar test based on periodic sub-sampling, also known as skip-sampling, is presented by Davidson and Rambaccussing (2015). Their testing procedure compares the memory estimator of the skip-sampled data with the estimated d from the original data.…”