Pawel Janus

New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels

We develop a new model for the multivariate covariance matrix dynamics based on daily return observations and daily realized covariance matrix kernels based on intraday data. Both types of data may be fat-tailed. We account for this by assuming a matrix-F distribution for the realized kernels, and a multivariate Student’s t distribution for the returns. Using generalized autoregressive score dynamics for the unobserved true covariance matrix, our approach automatically corrects for the effect of outliers and incidentally large observations, both in returns and in covariances. Moreover, by an appropriate choice of scaling of the conditional score function we are able to retain a convenient matrix formulation for the dynamic updates of the covariance matrix. This makes the model highly computationally efficient. We show how the model performs in a controlled simulation setting as well as for empirical data. In our empirical application, we study daily returns and realized kernels from 15 equities over the period 2001-2012 and find that the new model statistically outperforms (recently developed) multivariate volatility models, both in-sample and out-of-sample. We also comment on the possibility to use composite likelihood methods for estimation if desired.

New HEAVY Models for Fat-Tailed Realized Covariances and Returns

ABSTRACT We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Students t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.

A Quantile-based Realized Measure of Variation: New Tests for Outlying Observations in Financial Data

In this article we introduce a new class of test statistics designed to detect the occurrence of abnormal observations. It derives from the joint distribution of moment- and quantile-based estimators of power variation sigma^r, under the assumption of a normal distribution for the underlying data. Our novel tests can be applied to test for jumps and are found to be generally more powerful than widely used alternatives. An extensive empirical illustration for high-frequency equity data suggests that jumps can be more prevalent than inferred from existing tests on the second or third moment of the data.

Realized Wishart-Garch: A Score-Driven Multi-Asset Volatility Model

We propose a novel multivariate GARCH model that incorporates realized measures for the variance matrix of returns. The key novelty is the joint formulation of a multivariate dynamic model for outer-products of returns, realized variances and realized covariances. The updating of the variance matrix relies on the score function of the joint likelihood function based on Gaussian and Wishart densities. The dynamic model is parsimonious while each innovation still impacts all elements of the variance matrix. Monte Carlo evidence for parameter estimation based on different small sample sizes is provided. We illustrate the model with an empirical application to a portfolio of 15 U.S. financial assets.