We examine tests for jumps based on recent asymptotic results; we interpret the tests as Hausman-type tests. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabil-ities revealed by the confusion matrix comprised of jump classification probabil-ities. We identify a pitfall in applying the asymptotic approximation over an entire sample. Theoretical and Monte Carlo analysis indicates that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for 7 % of stock market price variance.

Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a “true ” or "best " measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high-low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by an average of implied volatilities of index options as measured by VIX.

Most good texts arise from the desire to leave one's stamp on a discipline by training future generations of students, coupled with the recognition that existing texts are inadequate in various respects. My motivation is no different. There is a real need for a concise and modern introductory forecasting text. A number of features distinguish this book. First, although it uses only elementary mathematics, it conveys a strong feel for the important advances made since the work of Box and Jenkins more than thirty years ago. In addition to standard models of trend, seasonality, and cycles, it touches – sometimes extensively – upon topics such as: data mining and in-sample overfitting statistical graphics and exploratory data analysis model selection criteria recursive techniques for diagnosing structural change nonlinear models, including neural networks regime-switching models unit roots and stochastic trends

Existing empirical literature on the risk-return relation uses a relatively small amount of conditioning information to model the conditional mean and conditional volatility of excess stock market returns. We use dynamic factor analysis for large datasets to summarize a large amount of economic information by few estimated factors, and find that three new factors- termed “volatility,” “risk premium,” and “real” factors- contain important information about one-quarter-ahead excess returns and volatility not contained in commonly used predictor variables. Our specifications predict 16-20 % of the one-quarter-ahead variation in excess stock market returns, and exhibit stable and statistically significant out-of-sample forecasting power. We also find a positive conditional risk-return correlation.

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We take a nonstructural time-series approach to modeling and forecasting daily average temperature in ten U.S. cities, and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market. The answer is, perhaps surprisingly, yes. Time series modeling reveals both strong conditional mean dynamics and conditional variance dynamics in daily average temperature, and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises. Most importantly, it adapts readily to produce the long-horizon forecasts of relevance in weather derivatives contexts. We produce and evaluate both point and distributional forecasts of average temperature, with some success. We conclude that additional inquiry into nonstructural weather forecasting methods, as relevant for weather derivatives, will likely prove useful. Key Words: Risk management; hedging; insurance; seasonality; average temperature; financial derivatives; density forecasting JEL Codes: G0, C1 Acknowledgments: For financial support we thank the National Science Foundation, the Wharton Financial Institutions Center, and the Wharton Risk Management and Decision Process Center. For helpful comments we thank Marshall Blume, Larry Brown, Jeff Considine, John Dutton, Ren Garcia, Stephen Jewson, Vince Kaminski, Paul Kleindorfer, Howard Kunreuther, Yu Li, Bob Livezey, Cliff Mass, Don McIsaac, Nour Meddahi, David Pozo, Matt Pritsker, S.T. Rao, Claudio Riberio, Til Schuermann and Yihong Xia. We are also grateful for comments by participants at the American Meteorological Society's Policy Forum on Weather, Climate and Energy. None of those thanked, of course, are responsible in any way for the outcome. Address corresponde...

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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuous-time jump-diffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines time-discretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jump-diffusion models with nonlinear characteristics and even non-analytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns.

This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.

sive overview of financial risk management from the point of view of both Wall Street and the Ivory Tower. Most usefully, ABCD discuss a number of recent developments in the econometrics of time varying risk that hold vast promise for risk management applications: the dynamic conditional correlation model of Engle (2002) which permits large-scale, flexi-ble modeling of conditional covariance matrices; the use of high-frequency data to measure realized variances and covariances that has been developed largely by the authors; and the modeling of the full distribution of conditional returns. In this discussion I will just offer a couple of comments and extensions to ABCD’s very well organized survey. Unconditional vs Conditional Risk ABCD discuss extensively the pros and cons of both unconditional and conditional (dynamic) measures of risk. There is however an additional source of risk dynamics that is ignored in the paper and that, in fact, has not been studied much in the literature. Most financial assets are managed over time and it is therefore more important to study the risks of dynamic investment strategies rather than the risks of static portfolios. Especially for supervision and regulation purposes, it matters more to forecast the risk of a portfolio taking into account