ONE DAY WORKSHOP ON FINANCE AND STATISTICS
Chicago, April 10, 2008

PROGRAM

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Thursday April 10 | Room 400, Gleacher Center

Time	Speaker	Title (click for abstract)
8:15 am		Breakfast
8:45am		Conference Opening
9:00am	Eric Renault	Efficient Minimum Distance Estimation with Multiple Rates of Convergence
9:45am	Viktor Todorov	Activity Signature Plots and the Generalized Blumenthal-Getoor Index
10:30am		Morning Break
11:00am	Eric Ghysels	News - Good or Bad - and its Impact on Volatility Predictions over Multiple Horizons
11:45am	Per Mykland	Inference for Continuous Semimartingales Observed at High Frequency: A General Approach
12:30pm		Lunch
2:00pm	Kenneth Singleton	Estimation and Evaluation of Conditional Asset Pricing Models
2:45pm	Lars Hansen	Modeling the Long Run
3:30pm		Afternoon Break
4:00pm	Vladimir Spokoiny	Adaptive Estimation of Time-Inhomogeneous Financial Time Series
4:45pm	Marc Hoffmann	Some Remarks on Volatility Representation under Microstructure Noise
5:30pm		Reception
6:30pm		Conference ends

ABSTRACTS

Efficient Minimum Distance Estimation with Multiple Rates of Convergence

Eric Renault (University of North Carolina, Chapel Hill)

This paper extends the asymptotic theory of GMM inference to allow sample counterparts of the estimating equations to converge at (multiple) rates, different from the usual square-root of the sample size. In this setting, we provide consistent estimation of the structural parameters. In addition, we define a convenient rotation in the parameter space (or reparametrization) which permits to disentangle the different rates of convergence. More precisely, we identify special linear combinations of the structural parameters associated with a specific rate of convergence. Finally, we demonstrate the validity of usual inference procedures, like the overidentification test and Wald test, with standard formulas. It is important to stress that both estimation and testing work without requiring the knowledge of the various rates. However, the assessment of these rates is crucial for (asymptotic) power considerations. Possible applications include econometric problems with two dimensions of asymptotics, due to trimming, tail estimation, infill asymptotic, social interactions, kernel smoothing or any kind of regularization. (Joint with Bertille Antoine).

Activity Signature Plots and the Generalized Blumenthal-Getoor Index

Viktor Todorov (Northwestern University)

We consider inference about the activity index of a general Ito semimartingale; the index is an extension of the Blumenthal-Getoor index for pure-jump Levy processes. We define a new concept termed the quantile activity signature function, which is constructed from discrete observations of a process evolving continuously in time. Under quite general regularity conditions, we derive the asymptotic properties of the function as the sampling frequency increases and show that it is a useful device for making inferences about the activity level of an Ito semimartingale. A simulation study confirms the theoretical results. One empirical application is from finance. It indicates that the classical model comprised of a continuous component plus jumps is more plausible than a pure-jump model for the spot $/DM exchange rate over 1986--1999. A second application pertains to internet traffic data at NASA servers. We find that a pure-jump model with no continuous component and paths of infinite variation is appropriate for modeling this data set. These two quite different empirical outcomees illustrate the discriminatory power of the methodology. (Joint with George Tauchen).

News - good or bad - and its impact on volatility predictions over multiple horizons

Eric Ghysels (University of North Carolina, Chapel Hill)

We examine whether the sign and magnitude of discretely sampled high frequency returns have impact on future volatility predictions. We first let the 'data speak', namely with minimal interference we capture the mapping between returns over short horizons and future volatility over longer horizons. Technically speaking, we introduce semi-parametric MIDAS regressions. Compared to the semi-parametric infinite ARCH estimation in Linton and Mammen (2005) we show that the asymptotic distribution of semi-parametric MIDAS regressions depends on the mixed data sampling scheme. Also novel is the parametric specification we consider to deal with for intra-daily/daily lags. In the empirical work we revisit the concept of news impact curves introduced by Engle and Ng (1993), in the current high frequency data environment of financial market time series. We find that moderately good (intra-daily) news reduces volatility (the next day), while both very good news (unusual high positive returns) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries we find have profound implications for current volatility prediction models that are based on in-sample asymptotic analysis developed over recent years. (With Xihong Chen).

Inference for Continuous Semimartingales Observed at High Frequency: A General Approach

Per Mykland (University of Chicago)

The econometric literature of high frequency data usually relies on moment estimators which are derived from assuming local constancy of volatility and related quantities. We here show that this first order approximation is not always valid if used naively. We find that such approximations require an ex post adjustment involving asymptotic likelihood ratios. These are given. Several examples (powers of volatility, leverage effect, ANOVA) are provided. The first order approximations in this study can be over the period of one observation, or over blocks of successive observations. The theory relies heavily on the interplay between stable convergence and measure change, and on asymptotic expansions for martingales. Practically, the procedure permits (1) the definition of estimators of hard to reach quantities, such as the leverage effect, of volatility, (2) the improvement in efficiency in classical estimators, and (3) easy analysis. (Joint with Lan Zhang).

Estimation and Evaluation of Conditional Asset Pricing Models

Kenneth Singleton (Stanford University)

This paper addresses two methodological issues that are central to the assessments of the goodness-of-fit of asset pricing models in which the pricing kernel is a conditionally affine function of a set of priced risk factors. First, presuming that GMM is used to estimate the parameters of the pricing kernel, how should the instrument set be chosen? For a wide class of moment-based tests of fit, including those that have been widely applied in the literature, we show that there is an optimal choice of instruments. Second, if a researcher has a specific alternative model of the pricing kernel in mind, is there an optimal choice of managed portfolios to use in constructing a test against this alternative? We show that, for the class of alternatives examined, there is an optimal set of test portfolios that give rise to the globally asymptotically efficient test in the sense of Bahadur (1967) and Geweke (1981). The proposed optimal tests of fit are implemented for several dynamic conditional factor models of excess returns on stocks. Once conditioning information is incorporated in an efficient manner, none of the candidate pricing kernels fits the conditional distributions of the returns on the Fama-French size and book-to-market portfolios. (Joint with Stefan Nagel).

Modeling the Long Run

Lars Hansen (University of Chicago)

In this paper I augment the toolkit for economic dynamics and asset valuation with methods that will reveal economic import of long-run stochastic structure. These tools enable informative decompositions of a model's dynamic implications for valuation. The methods I feature build in part on Perron-Frobenius theory applied to valuation operators that explicitly incorporate stochastic growth. The valuation operators are indexed by the gap of time between when a payoff is realized and when it is priced. Appropriately adapted Perron-Frobenius theory gives a characterization of the valuation behavior when this gap becomes large. Using such methods I provide operational decompositions of value implications of economic models including measures of parameter sensitivity and characterizations of long-run risk prices.

Adaptive Estimation of Time-Inhomogeneous Financial Time Series

Vladimir Spokoiny (Weierstrass Institute, Berlin)

This paper offers a new method for estimation and forecasting of the linear and nonlinear volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients may arbitrarily vary with time. Global parametric, smooth transition, and change-point models are special cases. The method is based on an adaptive pointwise selection of the largest interval of homogeneity with a given right-end point by a local change-point analysis. We construct locally adaptive estimates that can perform this task and investigate them both from the theoretical point of view and by Monte Carlo simulations. In the particular case of GARCH estimation, the proposed method is applied to stock-index series and is shown to outperform the standard parametric GARCH model.

Some Remarks on Volatility Representation under Microstructure Noise

Marc Hoffmann (Universite de Marne-la-Vallee)

We will review and discuss some aspects of microstruture noise when addressing volatility estimation from high frequency data. We will discuss an asymptotic representation of the (nonparametric) volatility, whether the asset modelling is understood from coarse-to-fine scales (i.e. semimartingale latent price corrupted by noise at high frequencies) or rather fine-to-coarse scales (i.e. microscopic agent based model of competing liquidity takers or providers whih diffuse at coarse scales). The particular case of (simple) additive microstructure noise enables to merge the two viewpoints, up to some rescaling. Depending on time, we will also briefly discuss the related problem of covariation estimation in this setting, when the data are genuinely asynchronous, attempting to address a definition of the (ill-posed) problem of lead-lag effect between two dependent assets, which has some importance if practical statistical arbitrage issues are considered. The body of informal results presented here are joint with Arnaud Gloter (Marne-la-Valle, Paris), Mathieu Rosenbaum (Marne-la-Vallee, Paris) and Nakahiro Yoshida (Tokyo).