The nexus between black and digital gold: evidence from US markets

In the context of the debate on cryptocurrencies as the ‘digital gold’, this study explores the nexus between the Bitcoin and US oil returns by employing a rich set of parametric and non-parametric approaches. We examine the dependence structure of the US oil market and Bitcoin through Clayton copulas, normal copulas, and Gumbel copulas. Copulas help us to test the volatility of these dependence structures through left-tailed, right-tailed or normal distributions. We collected daily data from 5 February 2014 to 24 January 2019 on Bitcoin prices and oil prices. The data on bitcoin prices were extracted from coinmarketcap.com. The US oil prices were collected from the Federal Reserve Economic Data source. Maximum pseudo-likelihood estimation was applied to the dataset and showed that the US oil returns and Bitcoin are highly vulnerable to tail risks. The multiplier bootstrap-based goodness-of-fit test as well as Kendal plots also suggest left-tail dependence, and this adds to the robustness of the results. The stationary bootstrap test for the partial cross-quantilogram indicates which quantile in the left tail has a statistically significant relationship between Bitcoin and US oil returns. The study has crucial implications in terms of portfolio diversification using cryptocurrencies and oil-based hedging instruments.

A Bootstrap Method to Test Granger-Causality in the Frequency Domain

We propose a bootstrap test for unconditional and conditional Granger-causality spectra in the frequency domain. Our test aims to detect if the causality at a particular frequency is systematically different from zero. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. At each frequency, we test the sample causality against the distribution of the median causality across frequencies estimated for that process. Via our procedure, we infer about the relationship between money stock and GDP in the Euro Area during the period 1999–2017. We point out that the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at low frequencies.

Computationally Efficient Bootstrap Expressions for Bandwidth Selection in Nonparametric Curve Estimation

Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed bootstrap). In these contexts, four new bandwidth parameter selectors are proposed based on closed bootstrap expressions of the MISE of the kernel density estimator (case 1) and two approximations of the kernel hazard rate estimation (case 2). These expressions turn out to be very useful since Monte Carlo approximation is no longer needed. Finally, these smoothing parameter selectors are empirically compared with the already existing ones via a simulation study.

Response to Qian et al (2017): Daily and seasonal climate variations are both critical in the evolution of species’ elevational range size

In their recent critique, Qian et al. (2017) claimed that the results of structural equation modeling analysis (SEM) in Chan et al. (2016) were flawed. Here, we show that the source of the difference in their re-analysis is that Qian et al. did not follow the standard, iterative process of SEM, which allows researchers to evaluate which model offers the best account of the data in both absolute and relative senses. Here, we provide step-by-step instructions to reproduce our published results. All of Qian et al.’s concerns regarding SEM can be put to rest. Moreover, in our original paper we used three distinct statistical methods—hierarchical partitioning, SEM, and stationary bootstrap—to show that different temporal scales of environmental variability can differentially impact the elevational range size (ERS) of species. It is time to move on to probing the pressing issue of how and why climatic variability impacts ERS.