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Title: Fractal methods for fractional cointegration Authors:  Ladislav Kristoufek - Institute of Information Theory and Automation, Czech Academy of Sciences (Czech Republic) [presenting]
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 $y_t=\alpha+\beta x_t + u_t,$ where $x_t \sim I(d)$ and $u_t \sim I(d-b)$ which implies $y_t \sim I(\max[d,d-b])$. The fractional cointegration requires $b>0$ while the standard cointegration $CI(1,1)$ assumes $x_t,y_t \sim I(1)$ and $u_t \sim I(0)$. We are interested in various combinations of $d$ and $b$ parameters ($0 \le d,b \le 1$, 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 ($\beta=0$ and $\beta \ne 0$). 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 $b<0.5$).