Estimating stochastic volatility diffusion using conditional moments of integrated volatility

We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.

Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

Coordinated analysis of delayed sprites with high-speed images and remote electromagnetic fields

Simultaneous measurements of high-altitude optical emissions and magnetic fields produced by sprite-associated lightning discharges enable a close examination of the link between low-altitude lightning processes and high-altitude sprite processes. We report results of the coordinated analysis of high-speed sprite video and wideband magnetic field measurements recorded simultaneously at Yucca Ridge Field Station and Duke University. From June to August 2005, sprites were detected following 67 lightning strokes, all of which had positive polarity. Our data showed that 46% of the 83 discrete sprite events in these sequences initiated more than 10 ms after the lightning return stroke, and we focus on these delayed sprites in this work. All delayed sprites were preceded by continuing current moments that averaged at least 11 kA km between the return stroke and sprites. The total lightning charge moment change at sprite initiation varied from 600 to 18,600 C km, and the minimum value to initiate long-delayed sprites ranged from 600 for 15 ms delay to 2000 C km for more than 120 ms delay. We numerically simulated electric fields at altitudes above these lightning discharges and found that the maximum normalized electric fields are essentially the same as fields that produce short-delayed sprites. Both estimated and simulation-predicted sprite initiation altitudes indicate that long-delayed sprites generally initiate around 5 km lower than short-delayed sprites. The simulation results also reveal that slow (5-20 ms) intensifications in continuing current can play a major role in initiating delayed sprites. Copyright 2008 by the American Geophysical Union.

Indexed Regulation

Seminal work by Weitzman (1974) revealed prices are preferred to quantities when marginal benefits are relatively flat compared to marginal costs. We extend this comparison to indexed policies, where quantities are proportional to an index, such as output. We find that policy preferences hinge on additional parameters describing the first and second moments of the index and the ex post optimal quantity level. When the ratio of these variables' coefficients of variation divided by their correlation is less than approximately two, indexed quantities are preferred to fixed quantities. A slightly more complex condition determines when indexed quantities are preferred to prices. Applied to climate change policy, we find that the range of variation and correlation in country-level carbon dioxide emissions and GDP suggests the ranking of an emissions intensity cap (indexed to GDP) compared to a fixed emission cap is not uniform across countries; neither policy clearly dominates the other.