An Alternative Approach to Measure Co-Movement between Two Time Series

Abstract

The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method. 2 of 24 multivariate GARCH, to estimate large covariance matrices, and Hafner [26] developed the GDCC model which is able to capture the asset-specific heterogeneity in the correlation structure.In this paper, an alternative way to look at correlations and co-movements is proposed by using the Hurst exponent. Along the paper, correlations, co-movements, etc. refer to cross-correlation, i.e., correlation between two different series (or assets). Introducing the HP of Two Series Hurst Exponent of a Time SeriesHurst exponent can be used to measure persistence as well as mean reversion properties in a time series. Introduced by H.E. Hurst in 1951 [27] to study the frequency of rain and drought in order to size the Nile River Dam, its application was extended not only to social sciences (see [28] for an interesting review) but also to meteorology [29], astrophysics [30], geography [31], medicine [32] or culturomics [33]. The first method to estimate the Hurst exponent was the R/S analysis [34]. However, as a consequence of a lack of accuracy of this methodology claimed by several authors [35-38] and its limited validity mainly for fractional Brownian motions [39], there has been an effort in the literature to provide new algorithms to improve the estimation. Some of these techniques are the Hudaks Semiparametric Method (GPH) [40], the Quasi Maximum Likelihood analysis (QML) [41], the Generalized Hurst Exponent (GHE) [42], Wavelets [43], the Centered Moving Average (CMA) [44], the Multifractal Detrended Fluctuation Analysis (MF-DFA) [45], the Lyapunov Exponent [46,47], Geometric Method-Based Procedures (GM) [48] and Fractal Dimension Algorithms (FD) [49].Among all of them, in this paper we will use the GHE algorithm, because it does not require to calculate ranges, it is not biased when applied to short series [49,50] and the calculation is simple.The GHE algorithm is based on the scaling properties of the following statistic [50]:

Statistical Arbitrage in Emerging Markets: A Global Test of Efficiency

“…The authors found that this new methodology gives better results than the classical methodologies such as the distance or the correlation method. In a recent contribution [54], these authors proposed an alternative method to correlation and cointegration called the HP method.…”

A New Look on Financial Markets Co-Movement through Cooperative Dynamics in Many-Body Physics

“…Different approaches have been used to measure co-movement, such us cross-correlation analysis (Akoum et al [ 28 ]), spatial techniques (Fernández-Aviles et al [ 38 ]), regression coefficient (Brooks and De Negro [ 36 ]), quantiles (Cappiello et al [ 39 ]), tail-dependence coefficient (Garcia and Tsafack [ 40 ]), copula approach (Rebodero [ 29 ]), time series analysis (Antonakakis et al [ 37 ]), shortfall-multidimensional scaling approach (Fernández-Aviles et al [ 41 ]), or a recent approach based in Hurst Exponent (Ramos Requena et al [ 42 ]). In this paper, we propose a new approach to study the co-movement of the whole market based on some functions borrowed from or based on physical particle systems, following our previous works on this topic (Clara Rahola et al [ 43 ], Sánchez Granero et al [ 44 ], Puertas et al [ 45 ]).…”

Exploring Arbitrage Strategies in Corporate Social Responsibility Companies

“…Financial literature has introduced different methodologies for pair selection. Important contributions are the distance method [52], those based on correlation [53] and cointegration [54], the copula method [55] or Hurst exponent based method [56,57].…”