Estimating long range dependence: finite sample properties and confidence intervals

By Rafal Weron. 2001

397 citations recorded by the source corpus.

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/S statistics and are very close to asymptotic values for the periodogram regression method.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/24a252e4548524ee12f40a00f4e9d74a8f4a0e5f

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Citations in the corpus

Simultaneous estimation of the parameters of the Hurst–Kolmogorov stochastic process (2011, methodology): “Weron (2002) discusses the properties of residuals of regression, R/S method and periodogram method.”
Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates (2017, background): “They indeed need a big amount of data and no asymptotic theory is derived, so that one should use a bootstrap in order to obtain confidence intervals for the estimates [25, 45].”
Rescaled Range Analysis and Detrended Fluctuation Analysis: Finite Sample Properties and Confidence Intervals (2010, methodology): “(4) Fluctuation F2DFA(υ , l), which is defined as F2DFA(υ , l) = 1 υ υ ∑ t=1 Y 2υ ,l(t), (5) AUCO Czech Economic Review, vol. 4, no. 3 238 scales as F2DFA(υ , l)∼ cυ2H(l), (6) where again c is a constant independent of υ (Weron 2002).”
Measuring capital market efficiency: Global and local correlations structure (2012, methodology): “Such a procedure is chosen because each of the methods is better suited for different types of processes both for Hurst exponent and fractal dimension estimation [46, 7, 30, 25].”
Some comments on Hurst exponent and the long memory processes on capital markets (2008, neutral): “[6,28].”
On Hurst exponent estimation under heavy-tailed distributions (2010, methodology): “Such result was already discussed in (Weron, 2002) where the confidence intervals are based on percentiles rather than standard deviations.”
Multi-scaling in finance (2007, background): “( 1999 ), Weron and Przybylowsciz ( 2000 ) and Weron ( 2002 )) and several alternative approaches have been proposed.”