Sample Size and Accuracy of Estimation of the Fractional Differencing Parameter

Abstract

Recent empirical studies on human performance in cognitive tasks have provided evidence of long-range dependence in psychological time series. ARFIMA (p, d, q) methodology, an extension of the traditional Box-Jenkins ARIMA modeling, allows estimation of the long-term dependence in the presence of any possible short-memory components. This article examines, by means of Monte Carlo experiments, sample size requirements for the accurate estimation of the long-memory parameter d and documents the quality of the estimates for time series of different length in various (0, d, 0) and (1, d, 1) models. We demonstrate that the conditional sum of squares estimation, a computationally convenient technique available in current versions of SAS for Windows, provides good finite-sample performance, comparable to that of ML. Furthermore, a minimum sample size for parsimonious planning of psychological experiments is recommended.

The Free-movement pattern Y-maze: A cross-species measure of working memory and executive function

“…Using the lag-1 autocorrelation function (ACF), it is possible to determine the relationship between successive tetragram sequences and identify whether dependency lasts (Bailey & Thompson, 2006). ACFs that rapidly decay, fluctuating around zero, are indicative of a completely random, or memoryless process (Stadnytska & Werner, 2006), i.e. a Markovian process (Reynolds, 2010).…”

Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques

“…The more asymmetric the time series is, the more uncertain is the estimated strength of long-range persistence. Spectral techniques that estimate the strength of long-range persistence are common in statistical time series analysis, particularly in the econometrics and physics communities, and their performance has been intensively investigated (Schepers et al 1992;Gallant et al 1994;Taqqu et al 1995;Mehrabi et al 1997;Wen and Sinding-Larsen 1997;Pilgram and Kaplan 1998;Taqqu and Teverovsky 1998;Heneghan and McDarby 2000;Velasco 2000;Weron 2001;Eke et al 2002;Delignieres et al 2006;Stadnytska and Werner 2006;Boutahar et al 2007;Mielniczuk and Wojdyłło 2007;Boutahar 2009;Faÿ et al 2009;Stroe-Kunold et al 2009; see also Tables 6 and 7). The most common approach in the literature is to fit models using MLE to time series that are characterized by short-and long-range dependence.…”

A Test of Memory: The Fish, The Mouse, The Fly And The Human

“…Drosophila were guided into a pipette tip and then tapped gently into the maze through a hole in the lid which could be moved over the maze to get flies in and on entry moved away from the maze to prevent escape. All animals were recorded in the maze in dim conditions (1-2 lux) for 1 h. As with our previous study, data were first output as a time series of arm entries and exits, normalised (proportions of total turns) and analysed according to 16 overlapping tetragrams (RLLR, LLRR, RRRL, etc.) of which particular note was taken with regard to search strategies termed alternations (RLRL, LRLR) and repetitions (LLLL, RRRR), having previously seen that these are most notably affected by different treatments.…”

“…Using the lag-1 autocorrelation function (ACF) it is possible to determine the relationship between successive tetragram sequences and identify if dependency lasts beyond the tetragram set. 15 ACFs that rapidly decay, fluctuating around zero, would be indicative of a completely random, or memoryless process 16 , i.e. a Markovian process 17 .…”