Estimating the degree of activity of jumps in high frequency data

We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.Comment: Published in at http://dx.doi.org/10.1214/08-AOS640 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

High frequency market microstructure noise estimates and liquidity measures

Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liquidity. We find that more liquid stocks based on financial characteristics have lower noise and noise-to-signal ratio measured from their high frequency returns. We then examine whether there exists a common, market-wide, factor in high frequency stock-level measurements of noise, and whether that factor is priced in asset returns.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS200 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is Brownian motion necessary to model high-frequency data?

This paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency. We provide two tests, one where the null hypothesis is that a continuous component is present, the other where the continuous component is absent, and the model is then driven by a pure jump process. When applied to high-frequency individual stock data, both tests point toward the need to include a continuous component in the model.Comment: Published in at http://dx.doi.org/10.1214/09-AOS749 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions

We develop and implement a technique for closed-form maximum likelihood estimation (MLE) of multifactor affine yield models. We derive closed-form approximations to likelihoods for nine Dai and Singleton (2000) affine models. Simulations show our technique very accurately approximates true (but infeasible) MLE. Using US Treasury data, we estimate nine affine yield models with different market price of risk specifications. MLE allows non-nested model comparison using likelihood ratio tests; the preferred model depends on the market price of risk. Estimation with simulated and real data suggests our technique is much closer to true MLE than Euler and quasi-maximum likelihood (QML) methods.

Bias in Estimating Multivariate and Univariate Diffusions

Published in Journal of Econometrics, 2011, https://doi.org/10.1016/j.jeconom.2010.12.006</p

Variable Selection for Portfolio Choice

We study asset allocation when the conditional moments of returns are partly predictable. Rather than first model the return distribution and subsequently characterize the portfolio choice, we determine directly the dependence of the optimal portfolio weights on the predictive variables. We combine the predictors into a single index that best captures time-variations in investment opportunities. This index helps investors determine which economic variables they should track and, more importantly, in what combination. We consider investors with both expected utility (mean-variance and CRRA) and non-expected utility (ambiguity aversion and prospect theory) objectives and characterize their market-timing, horizon effects, and hedging demands.

Nonparametric tests of the Markov hypothesis in continuous-time models

We propose several statistics to test the Markov hypothesis for $\beta$-mixing stationary processes sampled at discrete time intervals. Our tests are based on the Chapman--Kolmogorov equation. We establish the asymptotic null distributions of the proposed test statistics, showing that Wilks's phenomenon holds. We compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process, with alternatives consisting of models with a stochastic mean reversion level, stochastic volatility and jumps.Comment: Published in at http://dx.doi.org/10.1214/09-AOS763 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing for co-jumps in financial markets

In this paper, we introduce the notion of co-jumps within the co-features framework. We formulate a limiting theory of co-jumps and discuss their discrete sample properties. In the presence of idiosyncratic price jumps, we identify the notion of weak co-jumps. We illustrate the empirical relevance of the proposed framework via an empirical application using the components of the Dow Jones Industrial Average 30 index running from 1 January 2010 to 30 June 2012, sampled at a five-min frequency