An estimator of the ex-post covariation of log-prices under asynchronicity and microstructure noise is proposed. It uses the Cholesky factorization of the covariance matrix in order to exploit the heterogeneity in trading intensities to estimate the different parameters sequentially with as many observations as possible. The estimator is positive semidefinite by construction. We derive asymptotic results and confirm their good finite sample properties by means of a Monte Carlo simulation. In the application we forecast portfolio Value-at-Risk and sector risk exposures for a portfolio of 52 stocks. We find that the dynamic models utilizing the proposed high-frequency estimator provide statistically and economically superior forecasts.

In this paper we study various MIDAS models for which the future daily variance is directly related to past observations of intraday predictors. Our goal is to determine if there exists an optimal sampling frequency in terms of variance prediction. Via Monte Carlo simulations we show that in a world without microstructure noise, the best model is the one using the highest available frequency for the predictors. However, in the presence of microstructure noise, the use of very high-frequency predictors may be problematic, leading to poor variance forecasts. The empirical application focuses on two highly liquid assets (i.e., Microsoft and S&P 500). We show that, when using raw intraday squared log-returns for the explanatory variable, there is a “high-frequency wall” – or frequency limit – above which MIDAS-RV forecasts deteriorate or stop improving. An improvement can be obtained when using intraday squared log-returns sampled at a higher frequency, provided they are pre-filtered to account for the presence of jumps, intraday diurnal pattern and/or microstructure noise. Finally, we compare the MIDAS model to other competing variance models including GARCH, GAS, HAR-RV and HAR-RV-J models. We find that the MIDAS model – when it is applied on filtered data –provides equivalent or even better variance forecasts than these models. JEL: C22, C53, G12 / KEY WORDS: Variance Forecasting, MIDAS, High-Frequency Data.

RÉSUMÉ. Nous considérons dans cet article des modèles de régression MIDAS pour examiner l'influence de la fréquence d'échantillonnage des prédicteurs sur la qualité des prévisions de la volatilité quotidienne. L'objectif principal est de vérifier si l'information incorporée par les prédicteurs à haute fréquence améliore la qualité des précisions de volatilité, et si oui, s'il existe une fréquence d'échantillonnage optimale de ces prédicteurs en termes de prédiction de la variance. Nous montrons, via des simulations Monte Carlo, que dans un monde sans bruit de microstructure, le meilleur modèle est celui qui utilise des prédicteurs à la fréquence la plus élevée possible. Cependant, en présence de bruit de microstructure, l'utilisation des měmes prédicteurs à haute fréquence peut ětre problématique, conduisant à des prévisions pauvres de la variance. L'application empirique se concentre sur deux actifs très liquides (Microsoft et S & P 500). Nous montrons que, lors de l'utilisation des rendements intra-journaliers au carré pour la variable explicative, il y a un « mur à haute fréquence » – ou limite de fréquence – au-delà duquel les prévisions des modèles MIDAS-RV se détériorent ou arrětent de s'améliorer. Une amélioration pourrait ětre obtenue lors de l'utilisation des rendements au carré échantillonnés à une fréquence plus élevée, à condition qu'ils soient préfiltrés pour tenir compte de la présence des sauts, de la saisonnalité intra-journalière et/ou du bruit de microstructure. Enfin, nous comparons le modèle MIDAS à d'autres modèles de variance concurrents, y compris les modèles GARCH, GAS, HAR-RV et HAR-RV-J. Nous constatons que le modèle MIDAS – quand il est appliqué sur des données filtrées – fournit des prévisions de variance équivalentes ou měme meilleures que ces modèles.

Financial asset prices occasionally exhibit large changes. To deal with their occurrence, observed return series are assumed to consist of a conditionally Gaussian ARMA-GARCH type model contaminated by an additive jump component. In this framework, a new test for additive jumps is proposed. The test is based on standardized returns, where the first two conditional moments of the non-contaminated observations are estimated in a robust way. Simulation results indicate that the test has very good finite sample properties, i.e. correct size and high proportion of correct jump detection. The test is applied to daily returns and detects less than 1% of jumps for three exchange rates and between 1% and 3% of jumps for about 50 large capitalization stock returns from the NYSE. Once jumps have been filtered out, all series are found to be conditionally Gaussian. It is also found that simple GARCH-type models estimated using filtered returns deliver more accurate out-of sample forecasts of the conditional variance than GARCH and Generalized Autoregressive Score (GAS) models estimated from raw data.