Lukas Vacha

Co-movement of energy commodities revisited: Evidence from wavelet coherence analysis

In this paper, we contribute to the literature on energy market co-movement by studying its dynamics in the time-frequency domain. The novelty of our approach lies in the application of wavelet tools to commodity market data. A major part of economic time series analysis is done in the time or frequency domain separately. Wavelet analysis combines these two fundamental approaches allowing study of the time series in the time-frequency domain. Using this framework, we propose a new, model-free way of estimating time-varying correlations. In the empirical analysis, we connect our approach to the dynamic conditional correlation approach of Engle (2002) on the main components of the energy sector. Namely, we use crude oil, gasoline, heating oil, and natural gas on a nearest-future basis over a period of approximately 16 and 1/2years beginning on November 1, 1993 and ending on July 21, 2010. Using wavelet coherence, we uncover interesting dynamics of correlations between energy commodities in the time-frequency space.

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.

Volatility spillovers across petroleum markets

By using our newly defined measure, we detect and quantify asymmetries in the volatility spillovers of petroleum commodities: crude oil, gasoline, and heating oil. The increase in volatility spillovers after 2001 correlates with the progressive financialization of the commodities. Further, increasing spillovers from volatility among petroleum commodities substantially change their pattern after 2008 (the financial crisis and advent of tight oil production). After 2008, asymmetries in spillovers markedly declined in terms of total as well as directional spillovers. In terms of asymmetries we also show that overall volatility spillovers due to negative (price) returns materialize to a greater degree than volatility spillovers due to positive returns. An analysis of directional spillovers reveals that no petroleum commodity dominates other commodities in terms of general spillover transmission.

Modeling and Forecasting Exchange Rate Volatility in Time-Frequency Domain

This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the influence of different timescales on volatility forecasts. The decomposition of volatility into several timescales approximates the behaviour of traders at corresponding investment horizons. The proposed methodology is moreover able to account for impact of jumps due to a recently proposed jump wavelet two scale realized volatility estimator. We propose a realized Jump-GARCH models estimated in two versions using maximum likelihood as well as observation-driven estimation framework of generalized autoregressive score. We compare forecasts using several popular realized volatility measures on foreign exchange rate futures data covering the recent financial crisis. Our results indicate that disentangling jump variation from the integrated variation is important for forecasting performance. An interesting insight into the volatility process is also provided by its multiscale decomposition. We find that most of the information for future volatility comes from high frequency part of the spectra representing very short investment horizons. Our newly proposed models outperform statistically the popular as well conventional models in both one-day and multi-period-ahead forecasting.

Gold, Oil, and Stocks

We employ a wavelet approach and conduct a time-frequency analysis of dynamic correlations between pairs of key traded assets (gold, oil, and stocks) covering the period from 1987 to 2012. The analysis is performed on both intra-day and daily data. We show that heterogeneity in correlations across a number of investment horizons between pairs of assets is a dominant feature during times of economic downturn and financial turbulence for all three pairs of the assets under research. Heterogeneity prevails in correlations between gold and stocks. After the 2008 crisis, correlations among all three assets increase and become homogenous: the timing differs for the three pairs but coincides with the structural breaks that are identified in specific correlation dynamics. A strong implication emerges: during the period under research, and from a different-investment-horizons perspective, all three assets could be used in a well-diversified portfolio only during relatively short periods.

Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our time-frequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics.

Asymmetric volatility connectedness on the forex market

We show how bad and good volatility propagate through forex markets, i.e., we provide evidence for asymmetric volatility connectedness on forex markets. Using high-frequency, intra-day data of the most actively traded currencies over 2007 - 2015 we document the dominating asymmetries in spillovers that are due to bad rather than good volatility. We also show that negative spillovers are chiefly tied to the dragging sovereign debt crisis in Europe while positive spillovers are correlated with the subprime crisis, different monetary policies among key world central banks, and developments on commodities markets. It seems that a combination of monetary and real-economy events is behind the net positive asymmetries in volatility spillovers, while fiscal factors are linked with net negative spillovers.

Asymmetric Connectedness of Stocks: How Does Bad and Good Volatility Spill over the U.S. Stock Market?

Based on the negative and positive realized semivariances developed in Barndorff-Nielsen et al. (2010), we modify the volatility spillover index devised in Diebold and Yilmaz (2009). The resulting asymmetric volatility spillover indices are easy to compute and account well for negative and positive parts of volatility. We apply the modified indices on the 30 U.S. stocks with the highest market capitalization over the period 2004-2011 to study intra-market spillovers. We provide evidence of sizable volatility-spillover asymmetries and a markedly different pattern of spillovers during periods of economic ups and downs.Asymmetries in volatility spillovers are highly relevant to risk valuation and portfolio diversification strategies in financial markets. Yet, the large literature studying information transmission mechanisms ignores the fact that bad and good volatility may spill over at different magnitudes. This paper fills this gap with two contributions. One, we suggest how to quantify asymmetries in volatility spillovers due to bad and good volatility. Two, using high frequency data covering most liquid U.S. stocks in seven sectors, we provide ample evidence of the asymmetric connectedness of stocks. We universally reject the hypothesis of symmetric connectedness at the disaggregate level but in contrast, we document the symmetric transmission of information in an aggregated portfolio. We show that bad and good volatility is transmitted at different magnitudes in different sectors, and the asymmetries sizably change over time. While negative spillovers are often of substantial magnitudes, they do not strictly dominate positive spillovers. We find that the overall intra-market connectedness of U.S. stocks increased substantially with the increased uncertainty of stock market participants during the financial crisis.

Monte Carlo-based tail exponent estimator

In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002–2005 and 2006–2009, we estimate the tail exponent.

How does bad and good volatility spill over across petroleum markets

We detect and quantify asymmetries in volatility spillovers using the realized semivariances of petroleum commodities: crude oil, gasoline, and heating oil. During the 1987--2014 period we document increasing spillovers from volatility among petroleum commodities that substantially change after the 2008 financial crisis. The increase in volatility spillovers correlates with the progressive financialization of the commodities. In terms of asymmetries in spillovers we show that periods of increasing crude oil prices strongly correlate with dominating spillovers due to bad volatility. Overall, bad volatility due to negative returns spills over among petroleum commodities to a much larger extent than good volatility due to positive returns. After the 2008 financial crisis the asymmetries in spillovers markedly declined in terms of total as well as directional spillovers. An analysis of directional spillovers further reveals that no commodity dominates other commodities in terms of spillover transmission in general.