Showing papers by "Neil Shephard published in 2012"

Multivariate high‐frequency‐based volatility (HEAVY) models

Abstract: This paper introduces a new class of multivariate volatility models that utilizes high-frequency data. We discuss the models' dynamics and highlight their differences from multivariate GARCH models. We also discuss their covariance targeting speci…cation and provide closed-form formulas for multi-step forecasts. Estimation and inference strategies are outlined. Empirical results suggest that the HEAVY model outperforms the multivariate GARCH model out-of-sample, with the gains being particularly signi…cant at short forecast horizons. Forecast gains are obtained for both forecast variances and correlations.

Integer-valued Lévy processes and low latency financial econometrics

Abstract: Motivated by features of low latency data in financial econometrics we study in detail integer-valued Levy processes as the basis of price processes for high-frequency econometrics. We propose using models built out of the difference of two subordinators. We apply these models in practice to low latency data for a variety of different types of futures contracts.

Efficient and feasible inference for the components of financial variation using blocked multipower variation

Abstract: High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variationby the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

Basics of Levy processes

Abstract: This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”.

Robust inference on parameters via particle filters and sandwich covariance matrices

Abstract: Likelihood based estimation of the parameters of state space models can be carried out via a particle filter. In this paper we show how to make valid inference on such parameters when the model is incorrect. In particular we develop a simulation strategy for computing sandwich covariance matrices which can be used for asymptotic likelihood based inference. These methods are illustrated on some simulated data.

Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices

Abstract: Estimating the covariance and correlation between assets using high frequency data is chal- lenging due to market microstructure effects and Epps effects. In this paper we extend Xiu's univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Un- der stochastic volatility the resulting QML estimator is positive semi-definite, uses all available data, is consistent and asymptotically mixed normal. The quasi-likelihood is computed using a Kalman filter and optimised using a relatively simple EM algorithm which scales well with the number of assets. We derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence. We show how to make it achieve the non-parametric efficiency bound for this problem. The estimator is also analysed usingMonte Carlo methods and applied on equity data that are distinct in their levels of liquidity.

Efficient and feasible inference for the components of financial variation using blocked multipower variation

Abstract: High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variation by the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

Multivariate Rotated ARCH Models

Abstract: This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. The extension to DCC-type parameterizations is given, introducing the rotated conditional correlation (RCC) model. Inference for these mdoels is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on some SJIA stocks.

Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices

Abstract: Estimating the covariance and correlation between assets using high frequency data is challenging due to market microstructure effects and Epps effects. In this paper we extend Xiu’s univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting QML estimator is positive semi-definite, uses all available data, is consistent and asymptotically mixed normal. The quasi-likelihood is computed using a Kalman filter and optimised using a relatively simple EM algorithm which scales well with the number of assets. We derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence. We show how to make it achieve the non-parametric efficiency bound for this problem. The estimator is also analysed using Monte Carlo methods and applied on equity data that are distinct in their levels of liquidity.