We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar from 1991 to 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronge related to the presence of high values of returns in the series.
We empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion, as they show multi-scaling, high Hurst exponents and sharp price movements. We use the generalized Hurst exponent (GHE, $H(q)$) to show that although these time-series have strong cyclical components, the fluctuations exhibit persistent behaviour, i.e., $H(q)>0.5$. We investigate the effectiveness of the GHE as a predictive tool in a simple linear forecasting model, and study the forecast error as a function of $H(q)$, with $q=1$ and $q=2$. Our results suggest that the GHE can be used as prediction tool for these time series when the Hurst exponent is dynamically evaluated on rolling time windows of size $approx 50 - 100$ hours. These results are also compared to the case in which the cyclical components have been subtracted from the time series, showing the importance of cyclicality in the prediction power of the Hurst exponent.
The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities.
Technical trading rules have a long history of being used by practitioners in financial markets. Their profitable ability and efficiency of technical trading rules are yet controversial. In this paper, we test the performance of more than seven thousands traditional technical trading rules on the Shanghai Securities Composite Index (SSCI) from May 21, 1992 through June 30, 2013 and Shanghai Shenzhen 300 Index (SHSZ 300) from April 8, 2005 through June 30, 2013 to check whether an effective trading strategy could be found by using the performance measurements based on the return and Sharpe ratio. To correct for the influence of the data-snooping effect, we adopt the Superior Predictive Ability test to evaluate if there exists a trading rule that can significantly outperform the benchmark. The result shows that for SSCI, technical trading rules offer significant profitability, while for SHSZ 300, this ability is lost. We further partition the SSCI into two sub-series and find that the efficiency of technical trading in sub-series, which have exactly the same spanning period as that of SHSZ 300, is severely weakened. By testing the trading rules on both indexes with a five-year moving window, we find that the financial bubble from 2005 to 2007 greatly improve the effectiveness of technical trading rules. This is consistent with the predictive ability of technical trading rules which appears when the market is less efficient.
Although technical trading rules have been widely used by practitioners in financial markets, their profitability still remains controversial. We here investigate the profitability of moving average (MA) and trading range break (TRB) rules by using the Shanghai Stock Exchange Composite Index (SHCI) from May 21, 1992 through December 31, 2013 and Shenzhen Stock Exchange Composite Index (SZCI) from April 3, 1991 through December 31, 2013. The $t$-test is adopted to check whether the mean returns which are conditioned on the trading signals are significantly different from unconditioned returns and whether the mean returns conditioned on the buy signals are significantly different from the mean returns conditioned on the sell signals. We find that TRB rules outperform MA rules and short-term variable moving average (VMA) rules outperform long-term VMA rules. By applying Whites Reality Check test and accounting for the data snooping effects, we find that the best trading rule outperforms the buy-and-hold strategy when transaction costs are not taken into consideration. Once transaction costs are included, trading profits will be eliminated completely. Our analysis suggests that simple trading rules like MA and TRB cannot beat the standard buy-and-hold strategy for the Chinese stock exchange indexes.
When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross-correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multi-scale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross-correlation between crude oil and gold futures by taking into consideration the impact of the US dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the MF-DCCA method fails.
We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=sigma(t) omega(t)$ where the $r(t)$ are the daily returns of the market index and the $omega(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=sigma(t) omega(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.
Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 to investigate the statistical properties of price limit hits and the dynamical evolution of several important financial variables before stock price hits its limits. We compare the properties of up-limit hits and down-limit hits. We also divide the whole period into three bullish periods and three bearish periods to unveil possible differences during bullish and bearish market states. To uncover the impacts of stock capitalization on price limit hits, we partition all stocks into six portfolios according to their capitalizations on different trading days. We find that the price limit trading rule has a cooling-off effect (object to the magnet effect), indicating that the rule takes effect in the Chinese stock markets. We find that price continuation is much more likely to occur than price reversal on the next trading day after a limit-hitting day, especially for down-limit hits, which has potential practical values for market practitioners.
The new digital revolution of big data is deeply changing our capability of understanding society and forecasting the outcome of many social and economic systems. Unfortunately, information can be very heterogeneous in the importance, relevance, and surprise it conveys, affecting severely the predictive power of semantic and statistical methods. Here we show that the aggregation of web users behavior can be elicited to overcome this problem in a hard to predict complex system, namely the financial market. Specifically, our in-sample analysis shows that the combined use of sentiment analysis of news and browsing activity of users of Yahoo! Finance greatly helps forecasting intra-day and daily price changes of a set of 100 highly capitalized US stocks traded in the period 2012-2013. Sentiment analysis or browsing activity when taken alone have very small or no predictive power. Conversely, when considering a news signal where in a given time interval we compute the average sentiment of the clicked news, weighted by the number of clicks, we show that for nearly 50% of the companies such signal Granger-causes hourly price returns. Our result indicates a wisdom-of-the-crowd effect that allows to exploit users activity to identify and weigh properly the relevant and surprising news, enhancing considerably the forecasting power of the news sentiment.
In a recent paper [textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys. Rev. E 85, 066108 (2012)}], Cristelli textit{et al.} analysed relation between skewness and kurtosis for complex dynamical systems and identified two power-law regimes of non-Gaussianity, one of which scales with an exponent of 2 and the other is with $4/3$. Finally the authors concluded that the observed relation is a universal fact in complex dynamical systems. Here, we test the proposed universal relation between skewness and kurtosis with large number of synthetic data and show that in fact it is not universal and originates only due to the small number of data points in the data sets considered. The proposed relation is tested using two different non-Gaussian distributions, namely $q$-Gaussian and Levy distributions. We clearly show that this relation disappears for sufficiently large data sets provided that the second moment of the distribution is finite. We find that, contrary to the claims of Cristelli textit{et al.} regarding a power-law scaling regime, kurtosis saturates to a single value, which is of course different from the Gaussian case ($K=3$), as the number of data is increased. On the other hand, if the second moment of the distribution is infinite, then the kurtosis seems to never converge to a single value. The converged kurtosis value for the finite second moment distributions and the number of data points needed to reach this value depend on the deviation of the original distribution from the Gaussian case. We also argue that the use of kurtosis to compare distributions to decide which one deviates from the Gaussian more can lead to incorrect results even for finite second moment distributions for small data sets, whereas it is totally misleading for infinite second moment distributions where the difference depends on $N$ for all finite $N$.
