In the present work we investigate the multiscale nature of the correlations for high frequency data (1 minute) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of "local" Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.
Deep Dive into Multi-scale correlations in different futures markets.
In the present work we investigate the multiscale nature of the correlations for high frequency data (1 minute) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of “local” Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.
In recent years we have witnessed the development of a new branch of research on the edge between physics and economics. This new area, nowadays widely recognized in both the communities, goes under the name of econophysics. One of the most important achievement of this novel discipline has been to point out empirically that the stock market is far from being efficient: memory processes and feedbacks are present and they play a quite important role in the dynamics of this system. In particular, several studies have addressed the analysis of market fluctuations or logarithmic returns, defined as r(t) = ln[P r (t)/P r (t-1)], where P r (t) is the price of a certain market at time t. Interestingly, the results show that the shape of the probability distribution function (pdf), P , irrespective of the particular stock under consideration, displays a leptokurtic behaviour 1 , that is "fat" tails, whose asymptotic decay can be well approximated by a power law, P (r) ∼ r -β , with exponent β ∼ 3. This result is very important and in fact openly contrasts with the standard assumption that for a long time has ruled the academic world of theoretical economics, that is, the efficient market hypothesis (EMH) [3]. According to the EMH Send offprint requests to: marco.bartolozzi@gmf.com.au 1 The actual shape of the distribution of returns is still a matter of debate. Intriguing frameworks have been recently proposed by Tsallis [1] and Beck [2]. A more complete discussion on this important topic is beyond the scope of the present work.
the dynamics of market price movements are equivalent to that of white noise and, therefore, their pdf can be well represented by a Gaussian. In other words, the very large fluctuations observed in the empirical price movement distribution, and represented by the power law tails, should not exist (statistically). For a broader discussion on this subject and the field of econophysics the interested reader can refer to the books and reviews in Refs. [4,5,6,7,8,9,10].
The source of the “anomalous” behaviour in the market dynamics has to be related to inefficiencies, such as feedbacks in the price which, eventually, lead to very large fluctuations, such as crashes. It is obvious that the exploitation of these inefficiencies, even if for limited periods of time, becomes extremely important for traders and financial companies.
For a single asset, inefficiencies are also related to correlations in the price value over time. It is well known that first order or linear correlations can be neglected for most of the indices when looking at time scales longer than a few minutes [4,5]. This does not rule out the possibility of higher order correlations, but, in order to extract these, we need to make use of tools that are more sophisticated than the standard autocorrelation function. Moreover, we need to consider possible non-stationarities that may affect the time series: the dynamics of the stock market behaves differently according to different “environmental” conditions such as, for example, changes in the market regulation or in the trading mechanism itself.
Detrended fluctuation analysis (DFA), recently proposed by Peng at al. [11] in the context of DNA nucleotides sequences, has been developed in order to extract correlations from time series with local trends -that is, from non-stationary times series. This method is particulary relevant not only to finance but also to areas such as geophysics or biophysics -where non-stationarity is the rule rather than the exception. The DFA method, summarized in Sec. 2, is based on the calculation of the average variance related to a certain trend at different scales. This procedure leads to an estimation, via a scaling relation, of the Hurst exponent, H ∈ [0, 1], of the time series: for 0 ≤ H < 0.5 it is said that the behaviour of the time series is antipersistent, and conversely, persistent for 0.5 < H ≤ 1. For completely uncorrelated movements, as assumed by the EMH, we expect H = 0.5. Note that the idea of calculating persistency/antipersistency in time series through the scaling of the variance is not peculiar to the DFA but in fact dates back to the pioneering work of Hurst (and so we obtain the name Hurst exponent) in the context of reservoir control on the Nile river dam project, around 1907 [12,13].
In the present work we investigate the temporal evolution at different scales of the local Hurst exponent [14,15,16,17,18], where by the term “local” we indicate the Hurst exponent calculated at time t over a certain temporal window L that extends backward in time. This concept is very important for non-stationary and multiscale systems such as the stock market. Here, the dynamics of the trading can be influenced at different horizons by differences in the portfolio of strategies used by traders. In this case there is no reason to believe that H should remain the same for all t or that it would not vary if we calculated it using windows of a differen
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
