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Fractal methods for fractional cointegration

Ladislav Kristoufek 

Czech Academy of Sciences, Institute of Information Theory and Automation (UTIA), Pod Vodárenskou věží 4, Prague 18208, Czech Republic
Charles University in Prague, Ke Karlovu 5, Prague 12116, Czech Republic

Abstract

Detrended fluctuation analysis (DFA) and detrending moving average (DMA) methods are standardly used for fractional differencing parameter d estimation. Recently, the DFA and DMA based estimators of standard regression parameters have been proposed. The estimators possess some desirable properties with regards to long-range dependence, trends, seasonalities and heavy tails. We study properties of both estimators beyond the general fractional cointegration framework, i.e. we examine a simple model yt =α+β xt + ut, where xt ~ I(d) and ut ~ I(d-b), which implies yt ~ I(\max[d,d-b]). The fractional cointegration requires b>0, while the standard cointegration CI(1,1) assumes xt,yt ~ I(1) and ut ~ I(0). We are interested in various combinations of d and b parameters (0 ≤ d,b ≤ 1, i.e. we cover not only the fractional cointegration framework). We provide a broad Monte Carlo simulation study focusing on different time series lengths, combination of d and b parameters, and on possible spurious relationships. Specifically, we compare the estimators based on DFA and DMA with the standard OLS procedure under true and spurious relationships β=0 and β ≠ 0). Based on the bias, standard error and mean squared error of the estimators, the new procedures outperform OLS for various settings (e.g. with d=1 and b<0.5).

 

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Related papers

Presentation: Invited oral at Econophysics Colloquium 2017, Symposium C, by Ladislav Kristoufek
See On-line Journal of Econophysics Colloquium 2017

Submitted: 2017-03-07 11:17
Revised:   2017-03-30 07:27