Leverage effect in energy futures

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 long-term 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 moving-average 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.Comment: 19 pages, 2 figures, 5 table

Long-Term Dependence Characteristics of European Stock Indices

In this paper we show the degrees of persistence of the time series if eight European stock market indices are measured, after their lack of ergodicity and stationarity has been established. The proper identification of the nature of the persistence of financial time series forms a crucial step in deciding whether econometric modeling of such series might provide meaningful results. Testing for ergodicity and stationarity must be the first step in deciding whether the assumptions of numerous time series models are met. Our results indicate that ergodicity and stationarity are very difficult to establish in daily observations of these market indexes and thus various time-series models cannot be successfully identified. However, the measured degrees of persistence point to the existence of certain dependencies, most likely of a nonlinear nature, which, perhaps can be used in the identification of proper empirical econometric models of such dynamic time paths of the European stock market indexes. The paper computes and analyzes the long- term dependence of the equity index data as measured by global Hurst exponents, which are computed from wavelet multi-resolution analysis. For example, the FTSE turns out to be an ultra-efficient market with abnormally fast mean-reversion, faster than theoretically postulated by a Geometric Brownian Motion. Various methodologies appear to produce non-unique empirical measurement results and it is very difficult to obtain definite conclusions regarding the presence or absence of long term dependence phenomena like persistence or anti-persistence based on the global or homogeneous Hurst exponent. More powerful methods, such as the computation of the multifractal spectra of financial time series may be required. However, the visualization of the wavelet resonance coefficients and their power spectrograms in the form of localized scalograms and average scalegrams, forcefully assist with the detection and measurement of several nonlinear types of market price diffusion.Long-Term Dependence, European Stock Indices

A simple method for detecting chaos in nature

Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available

Long-Range Dependence in Daily Interest Rate

We employ a number of parametric and non-parametric techniques to establish the existence of long-range dependence in daily interbank o er rates for four countries. We test for long memory using classical R=S analysis, variance-time plots and Lo's (1991) modi ed R=S statistic. In addition we estimate the fractional di erencing parameter using Whittle's (1951) maximum likelihood estimator and we shu e the data to destroy long and short memory in turn, and we repeat our non-parametric tests. From our non-parametric tests we And strong evidence of the presence of long memory in all four series independently of the chosen statistic. We nd evidence that supports the assertion of Willinger et al (1999) that Lo's statistic is biased towards non-rejection of the null hypothesis of no long-range dependence. The parametric estimation concurs with these results. Our results suggest that conventional tests for capital market integration and other similar hypotheses involving nominal interest rates should be treated with cautio

Persistence of inflationary shocks: Implications for West African Monetary Union Membership

Plans are far advanced to form a second monetary union, the West African Monetary Zone (WAMZ), in Africa. While much attention is being placed on convergence criteria and preparedness of the five aspiring member states, less attention is being placed on the extent to which the dynamics of inflation in individual countries are (dis)similar. This paper aims to stimulate debate on the long term sustainability of the union by examining the dynamics of inflation within these countries. Using Fractional Integration (FI) methods, we establish that some significant differences exist among the countries. Shocks to inflation in Sierra Leone are non mean reverting; results for The Gambia, Ghana and Guinea-Bissau suggest some inflation persistence, despite being mean reverting. Some policy implications are discussed and some warnings are raised

Robust vetoes for gravitational-wave burst triggers using known instrumental couplings

The search for signatures of transient, unmodelled gravitational-wave (GW) bursts in the data of ground-based interferometric detectors typically uses `excess-power' search methods. One of the most challenging problems in the burst-data-analysis is to distinguish between actual GW bursts and spurious noise transients that trigger the detection algorithms. In this paper, we present a unique and robust strategy to `veto' the instrumental glitches. This method makes use of the phenomenological understanding of the coupling of different detector sub-systems to the main detector output. The main idea behind this method is that the noise at the detector output (channel H) can be projected into two orthogonal directions in the Fourier space -- along, and orthogonal to, the direction in which the noise in an instrumental channel X would couple into H. If a noise transient in the detector output originates from channel X, it leaves the statistics of the noise-component of H orthogonal to X unchanged, which can be verified by a statistical hypothesis testing. This strategy is demonstrated by doing software injections in simulated Gaussian noise. We also formulate a less-rigorous, but computationally inexpensive alternative to the above method. Here, the parameters of the triggers in channel X are compared to the parameters of the triggers in channel H to see whether a trigger in channel H can be `explained' by a trigger in channel X and the measured transfer function.Comment: 14 Pages, 8 Figures, To appear in Class. Quantum Gra

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi