Generalized Method of Integrated Moments for High‐Frequency Data

By Jia Li, D. Xiu. 2016

69 citations recorded by the source corpus.

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second‐step GMM estimation, which requires the correction of a high‐order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens‐type consistent specification test. These infill asymptotic results are based on a novel empirical‐process‐type theory for general integrated functionals of noisy semimartingale processes.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e84352927a31b03c04004cd9cd28b94fd6fb6186

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Citations in the corpus

Principal Component Analysis of High-Frequency Data (2016, methodology): “Among applications, Litterman and Scheinkman (1991) employed PCA to document a threefactor structure of the term structure of bond yields, labeling the first three components as the level, the slope, and the curvature factors.”
Exploiting the errors: A simple approach for improved volatility forecasting (2016, background): “In fact, in line with the results of Li and Xiu (2015), for most of the series the HAR models based on the noise-robust estimators do not systematically improve on the standard HAR model based on the 5-minute RV .”
Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, unknown): “Spot volatility estimation is relevant also for multiple-step approaches to perform inference on functionals that hinge on the volatility, see, for example, Kalnina and Xiu (2017) and Li and Xiu (2016).”