A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: An Application to High-Frequency Covariance Dynamics

Abstract

The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may severely underestimate correlations if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering correlations, (ii) market microstructure noise is taken into account, (iii) estimation is performed through standard maximum likelihood methods. Our empirical analysis, performed on 1-second NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for highfrequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons. . We are particularly grateful for suggestions we have received from Maria Elvira Mancino, Davide Delle Monache, Ivan Petrella, Fabrizio Venditti, Giampiero Gallo, Davide Pirino and participants to the IAAE 2017 conference in Sapporo, the 10 th SoFiE conference in New York and the VIECO 2017 conference in Wien. 1A large class of conditional covariance models have been proposed in the econometric literature and their use is widespread in risk and portfolio management at daily or lower frequencies. Popular multivariate dynamic time-series models include the class of multivariate extensions of the univariate GARCH model of Engle (1982) andBollerslev (1986) and the Dynamic Conditional Correlation (DCC) model of Engle (2002). A drawback of these models is that they are misspecified if data are recorded with observational noise and require synchronization in case data are irregularly spaced. As a consequence, they cannot be straightforwardly applied to intraday data, since high-frequency prices are contaminated by microstructure noise and assets are traded asynchronously. Both effects may lead to ignore a large portion of data and can significantly underestimate correlations. The problem of estimating and forecasting intraday volatilities and correlations is, however, of crucial importance in high-frequency finance. For instance, an high-frequency trader is interested in rebalancing the portfolio on an intraday basis and thus needs accurate shortterm covariance forecasts. Similarly, the study of the intraday dependencies of financial assets is useful to examine the reaction of the market to external information and has a theoretical relevance in market microstructure research.We contribute to the literature on intraday covariance estimation by proposing a modelling strategy that can handle both asynchronous trading and microstructure effects. High-frequency log-prices are modeled t...

Dynamic discrete copula models for high‐frequency stock price changes

“…The information available at the opening therefore has a relatively larger idiosyncratic component, explaining the lower dependence level at the start of the trading day. Similar patterns are found in Buccheri, Bormetti, Corsi, and Lillo (), for instance.…”

High-Frequency Lead-Lag Effects and Cross-Asset Linkages: A Multi-Asset Lagged Adjustment Model

“…The assumption of a constant instantaneous covariance matrix Σ in the efficient log-price process may be regarded as too restrictive, since there is well-established evidence that both volatilities and correlations exhibit strong intraday variation (cf. e.g Andersen and Bollerslev, 1997, Tsay, 2005, Bibinger et al, 2014, Buccheri et al, 2019a. However, by performing extensive Monte-Carlo simulations on a misspecified DGP with a time-varying covariance matrix, we show in Section (3.2) that two relevant properties hold.…”

DSGE Models with observation-driven time-varying volatility

“…The mean µ t and covariance Σ t are the conditional mean and covariance matrix of y t obtained from the Kalman filter for the state space model in ( 2) and (3). We refer the reader to Dell Monache et al ( 2016) and Buccheri et al (2017) for further applications of GAS timevarying parameters in the context of Kalman filtering. We note that in practice the score innovation s t is typically not available in closed form and it can be computed using numerical differentiation.…”