Modelling realized variance when returns are serially correlated

This article examines the impact of serial correlation in high frequency returns on the realized variance measure. In particular, it is shown that the realized variance measure yields a biased estimate of the conditional return variance when returns are serially correlated. Using 10 years of FTSE-100 minute by minute data we demonstrate that a careful choice of sampling frequency is crucial in avoiding substantial biases. Moreover, we find that the autocovariance structure (magnitude and rate of decay) of FTSE-100 returns at different sampling frequencies is consistent with that of an ARMA process under temporal aggregation. A simple autocovariance function based method is proposed for choosing the “optimal” sampling frequency, that is, the highest available frequency at which the serial correlation of returns has a negligible impact on the realized variance measure. We find that the logarithmic realized variance series of the FTSE-100 index, constructed using an optimal sampling frequency of 25 minutes, can be modelled as an ARFIMA process. Exogenous variables such as lagged returns and contemporaneous trading volume appear to be highly significant regressors and are able to explain a large portion of the variation in daily realized variance. -- Dieser Artikel untersucht die Auswirkungen von autokorrelierten Erträgen auf das Maß der realisierten Varianz bei hochfrequenten Daten über die Erträge. Es wird gezeigt, dass die realisierte Varianz ein verzerrter Schätzer für die bedingte Varianz der Erträge bei Vorliegen von Autokorrelation ist. Unter Verwendung eines zehnjährigen Datensatzes von Minutendaten des FTSE-100 wird dargestellt, dass eine sorgfältige Auswahl der Stichprobenfrequenz unabdingbar zur Vermeidung von Verzerrungen ist. Eine einfache Methode zur Bestimmung der optimalen Stichprobenfrequenz, basierend auf der Autokovarianzfunktion, wird vorgeschlagen. Diese ergibt sich als die höchste Frequenz, bei der die vorhandene Autokorrelation noch einen vernachlässigbaren Einfluss auf das Maß der realisierten Varianz hat. Für den betrachteten Datensatz ergibt sich eine optimale Frequenz von 25 Minuten. Unter Verwendung dieser Frequenz können die logarithmierten Erträge des FTSE-100 als ARFIMA Prozess modelliert werden.High frequency data,realized return variance,market microstructure,temporal aggregation,long memory,bootstrap

Three essays on the econometric analysis of high frequency financial data.

This thesis is motivated by the observation that the time series properties of financial security prices can vary fundamentally with their sampling frequency. Econometric models developed for low frequency data may thus be unsuitable for high frequency data and vice versa. For instance, while daily or weekly returns are generally well described by a martingale difference sequence, the dynamics of intra-daily, say, minute by minute, returns can be substantially more complex. Despite this apparent conflict between the behavior of high and low frequency data, it is clear that the two are intimately related and that high frequency data carries a wealth of information regarding the properties of the process, also at low frequency. The objective of this thesis is to deepen our understanding of the way in which high frequency data can be used in financial econometrics. In particular, we focus on (i) how to model high frequency security prices, and (ii) how to use high frequency data to estimate latent variables such as return volatility. One finding throughout the thesis is that the choice of sampling frequency is of fundamental importance as it determines both the dynamics and the information content of the data. A more detailed description of the chapters follows below.Macroeconomics -- Models;

A blocking and regularization approach to high dimensional realized covariance estimation

We introduce a regularization and blocking estimator for well-conditioned high-dimensional daily covariances using high-frequency data. Using the Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008a) kernel estimator, we estimate the covariance matrix block-wise and regularize it. A data-driven grouping of assets of similar trading frequency ensures the reduction of data loss due to refresh time sampling. In an extensive simulation study mimicking the empirical features of the S&P 1500 universe we show that the ’RnB’ estimator yields efficiency gains and outperforms competing kernel estimators for varying liquidity settings, noise-to-signal ratios, and dimensions. An empirical application of forecasting daily covariances of the S&P 500 index confirms the simulation results

Properties of realized variance for a pure jump process: calendar time sampling versus business time sampling

In this paper we study the impact of market microstructure effects on the properties of realized variance using a pure jump process for high frequency security prices. Closed form expressions for the bias and mean squared error of realized variance are derived under alternative sampling schemes. Importantly, we show that business time sampling is generally superior to the common practice of calendar time sampling in that it leads to a reduction in mean squared error. Using IBM transaction data we estimate the model parameters and determine the optimal sampling frequency for each day in the data set. The empirical results reveal a downward trend in optimal sampling frequency over the last 4 years with considerable day-to-day variation that is closely related to changes in market liquidity

Properties of bias corrected realized variance under alternative sampling schemes

In this paper I study the statistical properties of a bias corrected realized variance measure when high frequency asset prices are contaminated with market microstructure noise. The analysis is based on a pure jump process for asset prices and explicitly distinguishes among different sampling schemes, including calendar time, business time, and transaction time sampling. Two main findings emerge from the theoretical and empirical analysis. Firstly, based on the mean squared error criterion, a bias correction to realized variance allows for the more efficient use of higher frequency data than the conventional realized variance estimator. Secondly, sampling in business time or transaction time is generally superior to the common practice of calendar time sampling in that it leads to a further reduction in mean squared error. Using IBM transaction data, I estimate a 2.5 minute optimal sampling frequency for realized variance in calendar time which drops to about 12 seconds when a first order bias correction is applied. This results in a more than 65% reduction in mean squared error. If in addition prices are sampled in transaction time, a further reduction of about 20% can be achieved

Some properties of Neg-raising in three sign languages

Neg-raising, the phenomenon whereby a negation in the main clause of a complex construction is interpreted as if belonging to the embedded clause, has been intensively studied in spoken languages. The same cannot be said for sign languages. In this paper, we investigate the properties of Neg-raising constructions in three sign languages: French Sign Language, Italian Sign Language, and Sign Language of the Netherlands.We report on two syntactic tests we applied to disambiguate Neg-raising and non-Negraising readings, showing that Neg-raising constructions have similar properties in the three sign languages that we studied, as well as in comparable constructions in spoken languages. We also discuss some intricate headshake spreading patterns we found in Neg-raising constructions in Sign Language of the Netherlands, a non-manual dominant sign language

Barium & related stars and their white-dwarf companions II. Main-sequence and subgiant stars

Barium (Ba) dwarfs and CH subgiants are the less-evolved analogues of Ba and CH giants. They are F- to G-type main-sequence stars polluted with heavy elements by a binary companion when the latter was on the Asymptotic Giant Branch (AGB). This companion is now a white dwarf that in most cases cannot be directly detected. We present a large systematic study of 60 objects classified as Ba dwarfs or CH subgiants. Combining radial-velocity measurements from HERMES and SALT high-resolution spectra with radial-velocity data from CORAVEL and CORALIE, we determine the orbital parameters of 27 systems. We also derive their masses by comparing their location in the Hertzsprung-Russell diagram with evolutionary models. We confirm that Ba dwarfs and CH subgiants are not at different evolutionary stages and have similar metallicities, despite their different names. Additionally, Ba giants appear significantly more massive than their main-sequence analogues. This is likely due to observational biases against the detection of hotter main-sequence post-mass-transfer objects. Combining our spectroscopic orbits with the Hipparcos astrometric data, we derive the orbital inclinations and the mass of the WD companion for four systems. Since this cannot be done for all systems in our sample yet (but should be with upcoming Gaia data releases), we also analyse the mass-function distribution of our binaries. We can model this distribution with very narrow mass distributions for the two components and random orbital orientation on the sky. Finally, based on BINSTAR evolutionary models, we suggest that the orbital evolution of low-mass Ba systems can be affected by a second phase of interaction along the Red Giant Branch of the Ba star, impacting on the eccentricities and periods of the giants.Comment: Accepted for publication in A&A on the 5th of April, 201