Do jumps matter for volatility forecasting? Evidence from energy markets

This paper characterizes the dynamics of jumps and analyzes their importance for volatility forecasting. Using high-frequency data on four prominent energy markets, we perform a model-free decomposition of realized variance into its continuous and discontinuous components. We find strong evidence of jumps in energy markets between 2007 and 2012. We then investigate the importance of jumps for volatility forecasting. To this end, we estimate and analyze the predictive ability of several Heterogenous Autoregressive (HAR) models that explicitly capture the dynamics of jumps. Conducting extensive in-sample and out-of-sample analyses, we establish that explicitly modeling jumps does not significantly improve forecast accuracy. Our results are broadly consistent across our four energy markets, forecasting horizons, and loss functions

A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

Shock capturing scheme for steady, supersonic, isentropic flow

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, isentropic flow. The scheme incorporates numerical characteristic decomposition, is shock-capturing by design and incorporates space marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A finite difference scheme for steady, supersonic, two-dimensional, compressible flow of real gases

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, compressible flow of real gases. The scheme incorparates numerical characteristic decomposition, is shock-capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Comments on some recent measurements of anomalously steep N2O and O3tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N2O) and ozone (O3) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k−2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k−1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k−2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the “singularity spectrum” associated with a one-dimensional field composed of randomly spaced jumps in concentration.

Propagation of the Madden-Julian Oscillation through the Maritime Continent and scale interaction with the diurnal cycle of precipitation

The convectively active part of the Madden-Julian Oscillation (MJO) propagates eastward through the warm pool, from the Indian Ocean through the Maritime Continent (the Indonesian archipelago) to the western Pacific. The Maritime Continent's complex topography means the exact nature of the MJO propagation through this region is unclear. Model simulations of the MJO are often poor over the region, leading to local errors in latent heat release and global errors in medium-range weather prediction and climate simulation. Using 14 northern winters of TRMM satellite data it is shown that, where the mean diurnal cycle of precipitation is strong, 80% of the MJO precipitation signal in the Maritime Continent is accounted for by changes in the amplitude of the diurnal cycle. Additionally, the relationship between outgoing long-wave radiation (OLR) and precipitation is weakened here, such that OLR is no longer a reliable proxy for precipitation. The canonical view of the MJO as the smooth eastward propagation of a large-scale precipitation envelope also breaks down over the islands of the Maritime Continent. Instead, a vanguard of precipitation (anomalies of 2.5 mm day^-1 over 10^6 km^2) jumps ahead of the main body by approximately 6 days or 2000 km. Hence, there can be enhanced precipitation over Sumatra, Borneo or New Guinea when the large-scale MJO envelope over the surrounding ocean is one of suppressed precipitation. This behaviour can be accommodated into existing MJO theories. Frictional and topographic moisture convergence and relatively clear skies ahead of the main convective envelope combine with the low thermal inertia of the islands, to allow a rapid response in the diurnal cycle which rectifies onto the lower-frequency MJO. Hence, accurate representations of the diurnal cycle and its scale interaction appear to be necessary for models to simulate the MJO successfully.

Low and middle altitude cusp particle signatures for general magnetopause reconnection rate variations: 1. Theory

We present predictions of the signatures of magnetosheath particle precipitation (in the regions classified as open low-latitude boundary layer, cusp, mantle and polar cap) for periods when the interplanetary magnetic field has a southward component. These are made using the “pulsating cusp” model of the effects of time-varying magnetic reconnection at the dayside magnetopause. Predictions are made for both low-altitude satellites in the topside ionosphere and for midaltitude spacecraft in the magnetosphere. Low-altitude cusp signatures, which show a continuous ion dispersion signature, reveal "quasi-steady reconnection" (one limit of the pulsating cusp model), which persists for a period of at least 10 min. We estimate that “quasi-steady” in this context corresponds to fluctuations in the reconnection rate of a factor of 2 or less. The other limit of the pulsating cusp model explains the instantaneous jumps in the precipitating ion spectrum that have been observed at low altitudes. Such jumps are produced by isolated pulses of reconnection: that is, they are separated by intervals when the reconnection rate is zero. These also generate convecting patches on the magnetopause in which the field lines thread the boundary via a rotational discontinuity separated by more extensive regions of tangential discontinuity. Predictions of the corresponding ion precipitation signatures seen by midaltitude spacecraft are presented. We resolve the apparent contradiction between estimates of the width of the injection region from midaltitude data and the concept of continuous entry of solar wind plasma along open field lines. In addition, we reevaluate the use of pitch angle-energy dispersion to estimate the injection distance.

Time-variations in commodity price jumps

In this paper, we study jumps in commodity prices. Unlike assumed in existing models of commodity price dynamics, a simple analysis of the data reveals that the probability of tail events is not constant but depends on the time of the year, i.e. exhibits seasonality. We propose a stochastic volatility jump–diffusion model to capture this seasonal variation. Applying the Markov Chain Monte Carlo (MCMC) methodology, we estimate our model using 20 years of futures data from four different commodity markets. We find strong statistical evidence to suggest that our model with seasonal jump intensity outperforms models featuring a constant jump intensity. To demonstrate the practical relevance of our findings, we show that our model typically improves Value-at-Risk (VaR) forecasts.