•We explore the properties of the global banking network during 1978–2010.•Financial connectedness expands and contracts with the global cycle of capital flows.•Contrary to popular belief, ...connectedness in 2007 was not unusually high.•The severity of the 2008–2009 crisis has been driven by factors other than connectedness.•The 2008–2009 crisis stands out as an unusually large perturbation to the network.
We analyze the global banking network using data on cross-border banking flows for 184 countries during 1978–2010. We find that the density of the global banking network defined by these flows is pro-cyclical, expanding and contracting with the global cycle of capital flows. We also find that country connectedness in the network tends to rise before banking and debt crises and to fall in their aftermath. Despite a historically unique build-up in aggregate flows prior to the global financial crisis, network density in 2007 was comparable to earlier peaks. This suggests that factors other than connectedness, such as the location of the initial shock to the core of the network, have contributed to the severity of the crisis. The global financial crisis stands out as an unusually large perturbation to the global banking network, with indicators of network density in 2008 reaching all-time lows.
The weights of rational Bézier curves cannot be regarded as true independent shape factors since they do not enjoy invariance with respect to Moebius (i.e., rational linear) reparametrizations, which ...do not change the curve shape. However, the existence of such shape factors, also called shape invariants, is well-known. They are associated with each inner control point and are computed as the ratio of weight ratios for three consecutive control points. We show that these shape factors, in addition to their invariance to Moebius reparameterization, provide a more convenient shape control than the customary weights since they exert a more localized push/pull. Each shape factor amounts to that of the conic defined by a triplet of consecutive control points and weights. Thus, shape factors can be controlled in a geometric way using existing techniques for conics by setting the conic rho-factor via moving the associated shoulder point. Each shoulder point moves along a radial direction through its corresponding control point, furnishing a more practical shape handle than sliding the traditional weight points (aka Farin points) on the polygon legs.
•Shape factors of rational Bézier curves must be invariant to Moebius reparameterization.•They are defined as the ratio of weight ratios for three consecutive control points.•They provide a more convenient shape control (localized push/pull) than the weights.•Each factor is that of the conic defined by three consecutive control points and weights.•They can be controlled via the conic rho-factor, moving the associated shoulder point.
We revisit the rational cubic Bézier representation of conics, simplifying and expanding previous works, elucidating their connection, and making them more accessible. The key ingredient is the ...concept of conic associated with a given (planar) cubic Bézier polygon, resulting from an intuitive geometric construction: Take a cubic semicircle, whose control polygon forms a square, and apply the perspective that maps this square to the given polygon. Since cubic conics come from a quadratic version by inserting a base point, this conic admitting the polygon turns out to be unique. Therefore, detecting whether a cubic is a conic boils down to checking out whether it coincides with the conic associated with its control polygon. These two curves coincide if they have the same shape factors (aka, shape invariants) or, equivalently, the same oriented curvatures at the endpoints. Our results hold for any cubic polygon (with no three points collinear), irrespective of its convexity. However, only polygons forming a strictly convex quadrilateral define conics whose cubic form admits positive weights. Also, we provide a geometric interpretation for the added expressive power (over quadratics) that such cubics with positive weights offer. In addition to semiellipses, they encompass elliptical segments with rho-values over the negative unit interval.
•We present a systematic study on the rational cubic Bézier representation of conics.•The key ingredient is the conic associated with a given cubic Bézier polygon.•This conic results from applying a perspective to a semicircle embedded in a square.•A cubic is a conic if it coincides with this conic associated with the cubic polygon.•With positive weights, the cubic form duplicates the range of admissible rho-values.
Quantifying information dynamics in a nonlinear system is crucial in complex dynamics. The Mutual Information Matrix (MIM) method was developed to study nonlinear interactions in high-dimensional ...time series. In this paper, MIM analysis is extended from a Shannon entropy approach to a Rényi entropy one. Specifically, this paper presents the MIM for Rényi entropy with emphasis on the quadratic case. A global measure to quantify the total information shared between time series is defined and compared with the Shannon case. The main properties are illustrated by numerical simulations related to vector autoregressive fractionally integrated moving-average and sinusoidal models, and the methodology was applied to ozone multivariate time series of a meteorological monitoring network. Comparing both global measures, the proposed one gave different results in the nonlinear interaction quantification between stations than those based on Shannon entropy in the ozone monitoring network.
Carbon sequestration in soils under agricultural use can contribute to climate change mitigation. Spatial-temporal soil organic carbon (SOC) monitoring requires more efficient data acquisition. This ...study aims to evaluate the potential of spectral on-the-go proximal measurements to serve these needs. The study was conducted as a long-term field experiment. SOC values ranged between 14 and 25 g kg
due to different fertilization treatments. Partial least squares regression models were built based on the spectral laboratory and field data collected with two spectrometers (site-specific and on-the-go). Correction of the field data based on the laboratory data was done by testing linear transformation, piecewise direct standardization, and external parameter orthogonalization (EPO). Different preprocessing methods were applied to extract the best possible information content from the sensor signal. The models were then thoroughly interpreted concerning spectral wavelength importance using regression coefficients and variable importance in projection scores. The detailed wavelength importance analysis disclosed the challenge of using soil spectroscopy for SOC monitoring. The use of different spectrometers under varying soil conditions revealed shifts in wavelength importance. Still, our findings on the use of on-the-go spectroscopy for spatial-temporal SOC monitoring are promising.
As the recent crisis has forcefully suggested, understanding financial-market interconnectedness is of a paramount importance to explain systemic risk, stability and economic dynamics. In this paper, ...we address these issues along two related perspectives. First, we explore the statistical properties of the International Financial Network (IFN), defined as a weighted-directed graph where nodes are countries and links represent debtor–creditor relationships in equities and short/long-run debt. We investigate whether the 2008 financial crisis has resulted in a significant change in the topological properties of the IFN. Our findings suggest that the crisis caused not only a reduction in the amount of securities traded, but also induced changes in the topology of the network and in the time evolution of its statistical properties. This has happened, however, without changing the disassortative, core-periphery structure of the IFN architecture. Second, we perform an econometric study to examine the ability of network-based measures to explain cross-country differences in crisis intensity. We investigate whether the conclusion of previous studies showing that international connectedness is not a relevant predictor of crisis intensity may be reversed, once one explicitly accounts for the position of each country within the IFN. We show that higher interconnectedness reduces the severity of the crisis, as it allows adverse shocks to dissipate quicker. However, being central in the network may make countries that are not members of a rich club more vulnerable in times of crisis. Finally, we find strong evidence of nonlinear effects, once the high degree of heterogeneity that characterizes the IFN is taken into account.
Zhao et al. (Nonlin. Dyn. 88, 477-487, 2017) presented the mutual information matrix (MIM) analysis for the study of nonlinear interactions in multivariate time series as an extension of Random ...Matrix Theory analysis. They considered the histogram estimation of mutual information based on Shannon entropy for discrete distributions. This paper is motivated by the latter, extending MIM analysis from a nonparametric and probabilistic discrete approach to a parametric and probabilistic continuous approach. Specifically, this paper presents the MIM based on Maximum Likelihood Estimators (MLEs) for flexible and tractable families of continuous multivariate distributions, called multivariate skew-elliptical families of distributions. This method focus on multivariate skew-Gaussian and skew-
t
distributions that allow modeling skewness and heavy-tails, respectively. Performance of the proposed methodology is illustrated by numerical results given by sinusoidal and vector autoregressive fractionally integrated moving-average models, and applied to a meteorological monitoring network data set. Results show that the consideration of skewness and heavy-tails in the transformed ozone time series produced some differences in the MIM estimations compared with those obtained by applying histogram estimations to transformed data. Given that mutual information index (MII) increases in line with the number of bins for the histogram estimator, the proposed methodology based on MLEs considered more robust estimators with respect to the histogram ones to determine the MII of multivariate time series.
Recently, Bizzarri et al. (2021) discussed the so-called Pythagorean-hodograph curves of Tschirnhaus type, a generalization to higher degrees of Tschirnhausen cubic. We recall that these curves in ...Bézier form coincide with the typical curves introduced by Mineur et al. (1998), as well as with a classical family of sinusoidal spirals. Therefore, they all enjoy the same properties, such as the rational character of their offsets or the existence of only one curve (up to similarities) for each degree. By elucidating this connection among curves of Tschirnhaus type, typical curves, and sinusoidal spirals, we rederive several relevant results found by Bizzarri et al. (2021).
•We elucidate the connection between curves of Tschirnhaus type and previous models.•They coincide with the typical Bézier curves introduced by Mineur et al. (1998).•They are also segments of sinusoidal spirals belonging to a classical family.•Several properties are direct consequences of this connection or easily rederived.
The Self-Exciting Threshold Autoregressive model (SETAR) is non-linear and considers threshold values to model time series affected by regimes. It is extended through the Multivariate SETAR (MSETAR) ...model, where the threshold variable can also be a multivariate process. The stationary marginal density (smd) of an MSETAR process of order one corresponds to a Unified Skew-Normal density. In this paper, the smd of an MSETAR of order one process was considered to compute explicit expressions of differential entropy and Kullback–Leibler and Jeffrey’s divergences between two MSETAR(1) processes. In addition, two asymptotic tests based on divergences were built for statistical significance testing of the disparity between MSETAR(1) processes and the threshold coefficient matrix. Information measures considered involved high-dimensional integrals that likewise depended on multivariate cumulative density normal function. To solve these integrals, Genz’s algorithm was considered based on Cholesky decomposition and Monte Carlo approximation. Some numerical experiments and applications to fish condition factor and Chilean economic perception time series illustrate performance.
We combine data on international trade linkages with a network approach to map the global trading system as an interdependent complex network. This enables us to obtain indicators of how well ...connected a country is into the global trading system. We use these network‐based measures of connectedness to explain stock market returns during recent episodes of financial crisis. We find that a crisis is amplified if the epicenter country is better integrated into the trade network. However, target countries affected by such a shock are in turn better able to dissipate the impact if they are well integrated into the network. A network approach can help explain why the Mexican, Asian, and Russian financial crises were highly contagious, while the crises that originated in Venezuela and Argentina did not have such a virulent effect. We suggest that a network approach incorporating the cascading and diffusion of interdependent ripples when a shock hits a specific part of the global trade network provides us with an improved explanation of financial contagion. (JEL F10, F36, F40, G15)
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