Ladislav Kristoufek

On Hurst exponent estimation under heavy-tailed distributions

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and generalized Hurst exponent approach (GHE) estimate Hurst exponent on independent series with different heavy tails. For this purpose, we generate independent random series from stable distribution with stability exponent α changing from 1.1 (heaviest tails) to 2 (Gaussian normal distribution) and we estimate the Hurst exponent using the different methods. R/S and GHE prove to be robust to heavy tails in the underlying process. GHE provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size. Utilizing this result, we apply a novel approach of the intraday time-dependent Hurst exponent and we estimate the Hurst exponent on high frequency data for each trading day separately. We obtain Hurst exponents for S&P500 index for the period beginning with year 1983 and ending by November 2009 and we discuss the surprising result which uncovers how the market’s behavior changed over this long period.

Multifractal height cross-correlation analysis: A new method for analyzing long-range cross-correlations

We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek, T.: Multifractality of self-affine fractals, Physical Review A 44(4), 1991]. The method can be used to analyze long-range cross-correlations and multifractality between two simultaneously recorded series. We illustrate a power of the method on both simulated and real-world time series.

BitCoin meets Google Trends and Wikipedia : Quantifying the relationship between phenomena of the Internet era

Digital currencies have emerged as a new fascinating phenomenon in the financial markets. Recent events on the most popular of the digital currencies – BitCoin – have risen crucial questions about behavior of its exchange rates and they offer a field to study dynamics of the market which consists practically only of speculative traders with no fundamentalists as there is no fundamental value to the currency. In the paper, we connect two phenomena of the latest years – digital currencies, namely BitCoin, and search queries on Google Trends and Wikipedia – and study their relationship. We show that not only are the search queries and the prices connected but there also exists a pronounced asymmetry between the effect of an increased interest in the currency while being above or below its trend value.

What are the main drivers of the Bitcoin price? : evidence from wavelet coherence analysis

The Bitcoin has emerged as a fascinating phenomenon in the Financial markets. Without any central authority issuing the currency, the Bitcoin has been associated with controversy ever since its popularity, accompanied by increased public interest, reached high levels. Here, we contribute to the discussion by examining the potential drivers of Bitcoin prices, ranging from fundamental sources to speculative and technical ones, and we further study the potential influence of the Chinese market. The evolution of relationships is examined in both time and frequency domains utilizing the continuous wavelets framework, so that we not only comment on the development of the interconnections in time but also distinguish between short-term and long-term connections. We find that the Bitcoin forms a unique asset possessing properties of both a standard financial asset and a speculative one.

Measuring correlations between non-stationary series with DCCA coefficient

In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured by the fractional differencing parameter d). For a comparison, we also report the results for the standard Pearson correlation coefficient. The DCCA coefficient dominates the Pearson coefficient for non-stationary series.

Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient ρDMCA(λ) with a moving average window length λ. We analytically show that the coefficient ranges between −1 and 1 as a standard correlation does. In the simulation study, we show that the values of ρDMCA(λ) very well correspond to the true correlation between the analyzed series regardless the (non-)stationarity level. Dependence of the newly proposed measure on other parameters–correlation level, moving average window length and time series length–is discussed as well.

Commodity futures and market efficiency

We propose a comprehensive treatment of the leverage effect, i.e. the relationship between returns and volatility of a specific asset, focusing on energy commodities futures, namely Brent and WTI crude oils, natural gas and heating oil. After estimating the volatility process without assuming any specific form of its behavior, we find the volatility to be longterm dependent with the Hurst exponent on a verge of stationarity and non-stationarity. Bypassing this using by using the detrended cross-correlation and the detrending movingaverage cross-correlation coefficients, we find the standard leverage effect for both crude oil. For heating oil, the effect is not statistically significant, and for natural gas, we find the inverse leverage effect. Finally, we also show that none of the effects between returns and volatility is detected as the long-term cross-correlated one. These findings can be further utilized to enhance forecasting models and mainly in the risk management and portfolio diversification.

Can Google Trends search queries contribute to risk diversification

Portfolio diversification and active risk management are essential parts of financial analysis which became even more crucial (and questioned) during and after the years of the Global Financial Crisis. We propose a novel approach to portfolio diversification using the information of searched items on Google Trends. The diversification is based on an idea that popularity of a stock measured by search queries is correlated with the stock riskiness. We penalize the popular stocks by assigning them lower portfolio weights and we bring forward the less popular, or peripheral, stocks to decrease the total riskiness of the portfolio. Our results indicate that such strategy dominates both the benchmark index and the uniformly weighted portfolio both in-sample and out-of-sample.

Measuring capital market efficiency: Global and local correlations structure

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market situation. The proposed methodology is applied to a portfolio of 41 stock indices. We find that the Japanese NIKKEI is the most efficient market. From a geographical point of view, the more efficient markets are dominated by the European stock indices and the less efficient markets cover mainly Latin America, Asia and Oceania. The inefficiency is mainly driven by a local herding, i.e. a low fractal dimension.

Time-Frequency Dynamics of Biofuels-Fuels-Food System

For the first time, we apply the wavelet coherence methodology on biofuels (ethanol and biodiesel) and a wide range of related commodities (gasoline, diesel, crude oil, corn, wheat, soybeans, sugarcane and rapeseed oil). This way, we are able to investigate dynamics of correlations in time and across scales (frequencies) with a model-free approach. We show that correlations indeed vary in time and across frequencies. We find two highly correlated pairs which are strongly connected at low frequencies – ethanol with corn and biodiesel with German diesel – during almost the whole analyzed period (2003–2011). Structure of correlations remarkably changes during the food crisis — higher frequencies become important for both mentioned pairs. This implies that during stable periods, ethanol is correlated with corn and biodiesel is correlated with German diesel mainly at low frequencies so that they follow a common long-term trend. However, in the crisis periods, ethanol (biodiesel) is led by corn (German diesel) even at high frequencies (low scales), which implies that the biofuels prices react more rapidly to the changes in their producing factors.