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.

Carbon Markets: Past, Present, and Future

Carbon markets are substantial and they are expanding. There are many lessons from experiences over the past eight years: fewer free allowances, better management of market-sensitive information, and a recognition that trading systems require adjustments that have consequences for market participants and market confidence. Moreover, the emerging international architecture features separate emissions trading systems serving distinct jurisdictions. These programs are complemented by a variety of other types of policies alongside the carbon markets. This sits in sharp contrast to the integrated global trading architecture envisioned 15 years ago by the designers of the Kyoto Protocol and raises a suite of new questions. In this new architecture, jurisdictions with emissions trading have to decide how, whether, and when to link with one another, and policymakers overseeing carbon markets must confront how to measure the comparability of efforts among markets and relative to a variety of other policy approaches.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Carbon markets: Past, present, and future

© 2014 by Annual Reviews.Carbon markets are substantial and expanding. There are many lessons from experience over the past 9 years: fewer free allowances, careful moderation of low and high prices, and a recognition that trading systems require adjustments that have consequences for market participants and market confidence. Moreover, the emerging international architecture features separate emissions trading systems serving distinct jurisdictions. These programs are complemented by a variety of other types of policies alongside the carbon markets. This architecture sits in sharp contrast to the integrated global trading architecture envisioned 15 years ago by the designers of the Kyoto Protocol and raises a suite of new questions. In this new architecture, jurisdictions with emissions trading have to decide how, whether, and when to link with one another, and policy makers must confront how to measure both the comparability of efforts among markets and the comparability between markets and a variety of other policy approaches.