Spurious Dynamics Research Articles

Are correlations constant? Empirical and theoretical results on popular correlation models in finance

Abstract Multivariate GARCH models have been designed as an extension of their univariate counterparts. Such a view is appealing from a modeling perspective but imposes correlation dynamics that are similar to time-varying volatility. In this paper, we argue that correlations are quite different in nature. We demonstrate that the highly unstable and erratic behavior that is typically observed for the correlation among financial assets is to a large extent a statistical artifact. We provide evidence that spurious correlation dynamics occur in response to financial events that are sufficiently large to cause a structural break in the time-series of correlations. A measure for the autocovariance structure of conditional correlations allows us to formally demonstrate that the volatility and the persistence of daily correlations are not primarily driven by financial news but by the level of the underlying true correlation. Our results indicate that a rolling-window sample correlation is often a better choice for empirical applications in finance.

Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News

Applying tests for jumps to financial data sets can lead to an important number of spurious detections. Bursts of volatility are often incorrectly identified as jumps when the sampling is too sparse. At a higher frequency, methods robust to microstructure noise are required. We argue that whatever the jump detection test and the sampling frequency, a highly elevant number of spurious detections remain because of multiple testing issues. We propose a formal treatment based on an explicit thresholding on available test statistics. We prove that our method eliminates asymptotically all remaining spurious detections. In Dow Jones stocks between 2006 and 2008, spurious detections can represent up to 90% of the jumps detected initially. For the stocks considered, jumps are rare events, they do not cluster in time, and no cojump affects all stocks simultaneously, suggesting jump risk is diversifiable. We relate the remaining jumps to macroeconomic news, prescheduled company-specific announcements, and stories from news agencies which include a variety of unscheduled and uncategorized events. The vast majority of news do not cause jumps but may generate a market reaction of the form of bursts of volatility.

Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics

Modelers often need to quantify the rates at which zooplankton consume a variety of species, size classes and trophic types. Implicit in the equations used to describe the multiple resource functional response (i.e. how nutritional intake varies with resource densities) are assumptions that are not often stated, let alone tested. This is problematic because models are sensitive to the details of these formulations. Here, we enable modelers to make more informed decisions by providing them with a new framework for considering zooplankton feeding on multiple resources. We define a new classification of multiple resource responses that is based on preference, selection and switching, and we develop a set of mathematical diagnostics that elucidate model assumptions. We use these tools to evaluate the assumptions and biological dynamics inherent in published multiple resource responses. These models are shown to simulate different resource preferences, implied single resource responses, changes in intake with changing resource densities, nutritional benefits of generalism, and nutritional costs of selection. Certain formulations are further shown to exhibit anomalous dynamics such as negative switching and sub-optimal feeding. Such varied responses can have vastly different ecological consequences for both zooplankton and their resources; inappropriate choices may incorrectly quantify biologically-mediated fluxes and predict spurious dynamics. We discuss how our classes and diagnostics can help constrain parameters, interpret behaviors, and identify limitations to a formulation's applicability for both regional (e.g. High-Nitrate-Low-Chlorophyll regions comprising large areas of the Pacific) and large-scale applications (e.g. global biogeochemical or climate change models). Strategies for assessing uncertainty and for using the mathematics to guide future experimental investigations are also discussed.

Spurious dynamics in somatosensory cortex

Cortical networks are dynamical systems whose task is to process information. However, in addition to ‘intended’ dynamical behaviors, the sheer complexity of a cortical network's structure—regardless of its precise details—should generate additional ‘unintended’ dynamical behaviors. Dynamics observed in cortical network models and in the somatosensory cortex suggest that such spurious dynamical behaviors are likely to be pervasive but relatively simple, contributing to—rather than dominating—a network's response to stimuli. Spurious dynamics may be responsible for a variety of experimentally observed intriguing features of cortical dynamics. Because of their distributed origins and emergent nature, such dynamical features, while clearly identifiable, will resist attempts at identifying specific mechanisms to explain them. We describe some of the spurious dynamical phenomena associated with somatosensory cortical response to brushing stimulation, to illustrate how spurious dynamics can affect neurons’ functional properties, cortical stimulus representation and, ultimately, perception.

Computing global orbits of the forced spherical pendulum

Orbits of the spherical pendulum with time-periodic forcing are considered. A numerical framework is developed, which allows orbits to explore the entire “globe”: the spherical pendulum is considered as an invariant manifold in an ambient six-dimensional Euclidean space. The numerical integrator is the second-order Störmer–Verlet method coupled with the Shake–Rattle algorithm. The algorithm preserves numerically the phase space of the sphere, which is a manifold, to machine accuracy. Poincaré sections, restricted to the configuration space, are used to illustrate the transition from oscillatory behavior to chaotic solutions, as the amplitude of the pivot motion is changed. The qualitative change in the Poincaré sections from regular to chaotic behavior is in excellent qualitative agreement with corresponding computations of the Lyapunov exponents (LEs). The LEs are also computed using a novel variant of the Shake–Rattle algorithm. The results show that irregular behavior can explore the entire sphere—even at low forcing amplitudes—and therefore local methods which parameterize only part of the sphere are inadequate in general, and may lead to spurious dynamics. The numerical framework provides a tool for detailed investigation of the symmetric chaos of the forced spherical pendulum.

Dynamics of constant and variable stepsize methods for a nonlinear population model with delay

Hutchinson's equation is a reaction-diffusion model where the quadratic reaction term involves a delay. It is a natural extension of the logistic equation (no diffusion, no delay) and Fisher's equation (no delay), both of which have been used to illustrate the potential for spurious long-term dynamics in numerical methods. For the case where initial conditions and periodic boundary conditions are supplied, we look at the use of central differences in space and either Euler's method or the Improved Euler method in time. Our aim is to investigate the impact of the delay on the long-term behaviour of the scheme. After studying the fixed points of the methods in constant stepsize mode, we consider an adaptive time-stepping approach, using a standard local error control strategy. Applying ideas of Hall (1985) we are able to explain the fine detail of the time-step selection process.

Hyperviscous vortices

The structure of diffusing planar and axisymmetric vortices of the hyperviscous Navier-Stokes equations is studied for different orders of the dissipative operator. It is found that, except for the classical Newtonian case, the vorticity decays at large distances by means of oscillatory tails, containing circulation of alternating signs. This oscillation becomes stronger for large hyperviscosity orders, and the limit of infinite order is studied. It is argued that these solutions would become unstable for large enough Reynolds numbers, and may contribute non-trivial spurious dynamics to flow simulations using hyperviscosity.