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## Estimation and Testing for Dependence in Market Microstructure Noise

Ubukata, Masato; Oya, Kosuke
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica Formato: text/html
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This paper proposes new test statistics for the dependence and cross and auto covariance estimators of bivariate noise processes. It derives their asymptotic distributions and provides additional tests for the statistical significance of covariance estimators. Monte Carlo simulation shows that the covariance estimators and test statistics perform better in a finite sample. Further evidence from empirical illustration suggests that the covariance estimators and proposed test statistics are capable of capturing various dependence patterns in market microstructure noise. These results can shed more light on the sign of noise autocorrelation in the presence of market microstructure frictions such as bid-ask bounces and the clustering of order flow.

## Mesure et Prévision de la Volatilité pour les Actifs Liquides

Chaker, Selma
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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Le prix efficient est latent, il est contaminé par les frictions microstructurelles ou bruit. On explore la mesure et la prévision de la volatilité fondamentale en utilisant les données à haute fréquence. Dans le premier papier, en maintenant le cadre standard du modèle additif du bruit et le prix efficient, on montre qu’en utilisant le volume de transaction, les volumes d’achat et de vente, l’indicateur de la direction de transaction et la différence entre prix d’achat et prix de vente pour absorber le bruit, on améliore la précision des estimateurs de volatilité. Si le bruit n’est que partiellement absorbé, le bruit résiduel est plus proche d’un bruit blanc que le bruit original, ce qui diminue la misspécification des caractéristiques du bruit. Dans le deuxième papier, on part d’un fait empirique qu’on modélise par une forme linéaire de la variance du bruit microstructure en la volatilité fondamentale. Grâce à la représentation de la classe générale des modèles de volatilité stochastique, on explore la performance de prévision de différentes mesures de volatilité sous les hypothèses de notre modèle. Dans le troisième papier, on dérive de nouvelles mesures réalizées en utilisant les prix et les volumes d’achat et de vente. Comme alternative au modèle additif standard pour les prix contaminés avec le bruit microstructure...

## Bootstrapping high frequency data

Hounyo, Koomla Ulrich
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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Nous développons dans cette thèse, des méthodes de bootstrap pour les données financières de hautes fréquences. Les deux premiers essais focalisent sur les méthodes de bootstrap appliquées à l’approche de "pré-moyennement" et robustes à la présence d’erreurs de microstructure. Le "pré-moyennement" permet de réduire l’influence de l’effet de microstructure avant d’appliquer la volatilité réalisée. En se basant sur cette ap- proche d’estimation de la volatilité intégrée en présence d’erreurs de microstructure, nous développons plusieurs méthodes de bootstrap qui préservent la structure de dépendance et l’hétérogénéité dans la moyenne des données originelles. Le troisième essai développe une méthode de bootstrap sous l’hypothèse de Gaussianité locale des données financières de hautes fréquences. Le premier chapitre est intitulé: "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns". Nous proposons dans ce chapitre, des méthodes de bootstrap robustes à la présence d’erreurs de microstructure. Particulièrement nous nous sommes focalisés sur la volatilité réalisée utilisant des rendements "pré-moyennés" proposés par Podolskij et Vetter (2009)...

## The relationship between the volatility of returns and the number of jumps in financial markets

Cartea, Álvaro; Karyampas, Dimitrios
Tipo: Trabalho em Andamento Formato: application/pdf
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The contribution of this paper is two-fold. First we show how to estimate the volatility of high frequency log-returns where the estimates are not a affected by microstructure noise and the presence of Lévy-type jumps in prices. The second contribution focuses on the relationship between the number of jumps and the volatility of log-returns of the SPY, which is the fund that tracks the S&P 500. We employ SPY high frequency data (minute-by-minute) to obtain estimates of the volatility of the SPY log-returns to show that: (i) The number of jumps in the SPY is an important variable in explaining the daily volatility of the SPY log-returns; (ii) The number of jumps in the SPY prices has more explanatory power with respect to daily volatility than other variables based on: volume, number of trades, open and close, and other jump activity measures based on Bipower Variation; (iii) The number of jumps in the SPY prices has a similar explanatory power to that of the VIX, and slightly less explanatory power than measures based on high and low prices, when it comes to explaining volatility; (iv) Forecasts of the average number of jumps are important variables when producing monthly volatility forecasts and, furthermore, they contain information that is not impounded in the VIX.

## Efficient estimation using the characteristic function : theory and applications with high frequency data

Kotchoni, Rachidi
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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Nous abordons deux sujets distincts dans cette thèse: l'estimation de la volatilité des prix d'actifs financiers à partir des données à haute fréquence, et l'estimation des paramétres d'un processus aléatoire à partir de sa fonction caractéristique. Le chapitre 1 s'intéresse à l'estimation de la volatilité des prix d'actifs. Nous supposons que les données à haute fréquence disponibles sont entachées de bruit de microstructure. Les propriétés que l'on prête au bruit sont déterminantes dans le choix de l'estimateur de la volatilité. Dans ce chapitre, nous spécifions un nouveau modèle dynamique pour le bruit de microstructure qui intègre trois propriétés importantes: (i) le bruit peut être autocorrélé, (ii) le retard maximal au delà duquel l'autocorrélation est nulle peut être une fonction croissante de la fréquence journalière d'observations; (iii) le bruit peut avoir une composante correlée avec le rendement efficient. Cette dernière composante est alors dite endogène. Ce modèle se différencie de ceux existant en ceci qu'il implique que l'autocorrélation d'ordre 1 du bruit converge vers 1 lorsque la fréquence journalière d'observation tend vers l'infini. Nous utilisons le cadre semi-paramétrique ainsi défini pour dériver un nouvel estimateur de la volatilité intégrée baptisée "estimateur shrinkage". Cet estimateur se présente sous la forme d'une combinaison linéaire optimale de deux estimateurs aux propriétés différentes...

## Estimation of Asset Volatility and Correlation Over Market Microstructure Noise in High-Frequency Data

Yevstihnyeyev, Roman
Fonte: Harvard University Publicador: Harvard University
Tipo: Thesis or Dissertation; text Formato: application/pdf
Português
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Accurate measurement of asset return volatility and correlation is an important problem in financial econometrics. The presence of market microstructure noise in high-frequency data complicates such estimations. This study extends a prior application of a model-based volatility estimator with autocorrelated market microstructure noise to estimation of correlation. The model is applied to a high-frequency dataset including a stock and an index, and the results are compared to some existing models. This study supports previous findings that including an autocorrelation factor produces an estimator potentially less vulnerable to market microstructure noise, and finds that the same is true about the extended correlation estimator that is introduced here.

## Modeling microstructure noise with mutually exciting point processes

Bacry, E.; Delattre, S.; Hoffmann, M.; Muzy, J. F.
Tipo: Artigo de Revista Científica
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We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.; Comment: 31 pages, 8 figures

## Parametric Inference for Nonsynchronously Observed Diffusion Processes in the Presence of Market Microstructure Noise

Ogihara, Teppei
Tipo: Artigo de Revista Científica
Português
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We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of maximum-likelihood- and Bayes-type estimators based on it. We also prove the local asymptotic normality of the model and asymptotic efficiency of our estimator when the diffusion coefficients are constant and noise follows a normal distribution. We conjecture that our estimator is asymptotically efficient even when the latent process is a general diffusion process. An estimator for the quadratic covariation of the latent process is also constructed. Some numerical examples show that this estimator performs better compared to existing estimators of the quadratic covariation.; Comment: 39 pages

## On the inference about the spectra of high-dimensional covariance matrix based on noisy observations-with applications to integrated covolatility matrix inference in the presence of microstructure noise

Xia, Ningning; Zheng, Xinghua
Tipo: Artigo de Revista Científica
Português
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In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance matrix under such a situation, we establish an asymptotic relationship that describes how the limiting spectral distribution of (true) sample covariance matrices depends on that of information-plus-noise-type sample covariance matrices. As an application, we consider the inference about the spectra of integrated covolatility (ICV) matrices of high-dimensional diffusion processes based on high-frequency data with microstructure noise. The (slightly modified) pre-averaging estimator is an information-plus-noise-type covariance matrix, and the aforementioned result, together with a (generalized) connection between the spectral distribution of true sample covariance matrices and that of the population covariance matrix, enables us to propose a two-step procedure to estimate the spectral distribution of ICV for a class of diffusion processes. An alternative estimator is further proposed, which possesses two desirable properties: it eliminates the impact of microstructure noise, and its limiting spectral distribution depends only on that of the ICV through the standard Mar\v{c}enko-Pastur equation. Numerical studies demonstrate that our proposed methods can be used to estimate the spectra of the underlying covariance matrix based on noisy observations.

## A simple microstructure return model explaining microstructure noise and Epps effects

Saichev, A.; Sornette, D.
Tipo: Artigo de Revista Científica
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We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of microstructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time scale used to estimate it. Paradoxically, the Epps effect states that cross correlations between asset returns are increasing functions of the time scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time scale in the presence of the long memory process (i).; Comment: 31 pages + 19 figures

## Discerning Non-Stationary Market Microstructure Noise and Time-Varying Liquidity in High Frequency Data

Chen, Richard Y.; Mykland, Per A.
Tipo: Artigo de Revista Científica
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In this paper, we investigate the implication of non-stationary market microstructure noise to integrated volatility estimation, provide statistical tools to test stationarity and non-stationarity in market microstructure noise, and discuss how to measure liquidity risk using high frequency financial data. In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator, and design three test statistics by exploiting the edge effects and asymptotic approximation. The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptions respectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013. As byproducts, functional dependence and endogenous market microstructure noise are briefly discussed. Simulation studies corroborate our theoretical results. Our empirical study indicates the prevalence of non-stationary market microstructure noise in the New York Stock Exchange.

## Lower bounds for volatility estimation in microstructure noise models

Munk, Axel; Schmidt-Hieber, Johannes
Tipo: Artigo de Revista Científica
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In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. Three different models are considered. Our technique is based on a general inequality for Kullback-Leibler divergence of multivariate normal random variables and spectral analysis of the processes. The derived lower bounds are indeed optimal. Upper bounds can be found in Munk and Schmidt-Hieber [18]. Our major finding is that the Gaussian microstructure noise introduces an additional degree of ill-posedness for each model, respectively.; Comment: 16 pages

## High frequency market microstructure noise estimates and liquidity measures

Aït-Sahalia, Yacine; Yu, Jialin
Tipo: Artigo de Revista Científica
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Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liquidity. We find that more liquid stocks based on financial characteristics have lower noise and noise-to-signal ratio measured from their high frequency returns. We then examine whether there exists a common, market-wide, factor in high frequency stock-level measurements of noise, and whether that factor is priced in asset returns.; Comment: Published in at http://dx.doi.org/10.1214/08-AOAS200 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## Statistical Properties of Microstructure Noise

Jacod, Jean; Li, Yingying; Zheng, Xinghua
Tipo: Artigo de Revista Científica
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We study the estimation of moments and joint moments of microstructure noise. Estimators of arbitrary order of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of auto-covariances and auto-correlations of the noise. Simulation studies demonstrate excellent performance of our estimators even in the presence of jumps and irregular observation times. Empirical studies reveal (moderate) positive auto-correlation of the noise for the stocks tested.

## Volatility Inference in the Presence of Both Endogenous Time and Microstructure Noise

Li, Yingying; Zhang, Zhiyuan; Zheng, Xinghua
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this article we consider the volatility inference in the presence of both market microstructure noise and endogenous time. Estimators of the integrated volatility in such a setting are proposed, and their asymptotic properties are studied. Our proposed estimator is compared with the existing popular volatility estimators via numerical studies. The results show that our estimator can have substantially better performance when time endogeneity exists.

## Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps

Podolskij, Mark; Vetter, Mathias
Tipo: Artigo de Revista Científica
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We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower variation is proven. Under further assumptions we prove stable convergence of our estimates with the optimal rate $n^{-{1}/{4}}$. Moreover, we construct estimates which are robust to finite activity jumps.; Comment: Published in at http://dx.doi.org/10.3150/08-BEJ167 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

## Model checks for the volatility under microstructure noise

Vetter, Mathias; Dette, Holger
Tipo: Artigo de Revista Científica
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We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent. The concept of preaveraging is used to construct new tests, which do not suffer from these drawbacks. These tests are based on a Kolmogorov-Smirnov or Cramer-von-Mises functional of an integrated stochastic process, for which weak convergence to a (conditional) Gaussian process is established. The finite sample properties of a bootstrap version of the test are illustrated by means of a simulation study.; Comment: Published in at http://dx.doi.org/10.3150/11-BEJ384 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

## Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise

Reiß, Markus
Tipo: Artigo de Revista Científica
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The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $\sigma$. As an application, simple rate-optimal estimators of the volatility and efficient estimators of the integrated volatility are constructed.

## On-line Spot Volatility-Estimation and Decomposition with Nonlinear Market Microstructure Noise Models

Dahlhaus, Rainer; Neddermeyer, Jan C.
Tipo: Artigo de Revista Científica
Português
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A technique for on-line estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. Furthermore, a nonlinear market microstructure noise model is proposed that reproduces several stylized facts of high-frequency data. A computationally efficient particle filter is used that allows for the approximation of the unknown efficient prices and, in combination with a recursive EM algorithm, for the estimation of the volatility curve. We neither assume that the transaction times are equidistant nor do we use interpolated prices. We also make a distinction between volatility per time unit and volatility per transaction and provide estimators for both. More precisely we use a model with random time change where spot volatility is decomposed into spot volatility per transaction times the trading intensity - thus highlighting the influence of trading intensity on volatility.; Comment: 10 figures

Ryu, Angela