Mathias Vetter - Academia.edu (original) (raw)

Papers by Mathias Vetter

Research paper thumbnail of The null hypothesis of (common) jumps in case of irregular and asynchronous observations

Scandinavian Journal of Statistics

This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for t... more This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular observations, sampled at different frequencies. We develop central limit theorems for the statistics under the respective null hypotheses and apply bootstrap procedures to assess the limiting distributions. Further we define corrected statistics to improve the finite sample performance. Simulations show that the test based on our corrected statistic yields good results and even outperforms existing tests in the case of regular observations.

Research paper thumbnail of Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale

Stochastic Processes and their Applications

Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prov... more Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prove weak convergence of a normalized truncated empirical distribution function of the Lévy measure to a Gaussian process. In contrast to competing procedures, our estimator works for processes with a non-vanishing diffusion component and under simple assumptions on the jump process.

Research paper thumbnail of Laws of large numbers for Hayashi–Yoshida-type functionals

Finance and Stochastics

In high-frequency statistics and econometrics sums of functionals of increments of stochastic pro... more In high-frequency statistics and econometrics sums of functionals of increments of stochastic processes are commonly used and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. Inspired by the famous Hayashi-Yoshida estimator for the quadratic covariation process based on two asynchronously observed stochastic processes we investigate similar sums based on increments of two asynchronously observed stochastic processes for general functionals. We find that our results differ from corresponding results in the setting of equidistant and synchronous observations which has been well studied in the literature. Further we observe that in the setting of asynchronous observations the asymptotic behaviour is not only determined by the nature of the functional but also depends crucially on the asymptotics of the observation scheme.

Research paper thumbnail of Testing for simultaneous jumps in case of asynchronous observations

Bernoulli

This paper proposes a novel test for simultaneous jumps in a bivariate Itô semimartingale when ob... more This paper proposes a novel test for simultaneous jumps in a bivariate Itô semimartingale when observation times are asynchronous and irregular. Inference is built on a realized correlation coefficient for the jumps of the two processes which is estimated using bivariate power variations of Hayashi-Yoshida type without an additional synchronization step. An associated central limit theorem is shown whose asymptotic distribution is assessed using a bootstrap procedure. Simulations show that the test works remarkably well in comparison with the much simpler case of regular observations.

Research paper thumbnail of Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process

Bernoulli

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process... more This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in the jump measure of an Itō semimartingale are constructed. Whenever limiting distributions depend in a complicated way on the unknown jump measure, empirical quantiles are obtained using a multiplier bootstrap scheme. An extensive simulation study shows a good performance of our tests in finite samples.

Research paper thumbnail of Nonparametric change-point analysis of volatility

The Annals of Statistics

In this work, we develop change-point methods for statistics of highfrequency data. The main inte... more In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameters of fractional volatility processes. A simulation study is conducted to demonstrate the performance of our methods in finite-sample applications.

Research paper thumbnail of A note on central limit theorems for quadratic variation in case of endogenous observation times

Electronic Journal of Statistics

This paper is concerned with a central limit theorem for quadratic variation when observations co... more This paper is concerned with a central limit theorem for quadratic variation when observations come as exit times from a regular grid. We discuss the special case of a semimartingale with deterministic characteristics and finite activity jumps in detail and illustrate technical issues in more general situations.

Research paper thumbnail of Estimation of integrated volatility of volatility with applications to goodness-of-fit testing

Bernoulli, 2015

In this paper, we are concerned with nonparametric inference on the volatility of volatility proc... more In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on increments of spot volatility estimators. Some of those are positive by construction, others are bias corrected in order to attain the optimal rate n −1/4. Associated central limit theorems are proven which can be widely used in practice, as they are the key to essentially all tools in model validation for stochastic volatility models. As an illustration we give a brief idea on a goodness-of-fit test in order to check for a certain parametric form of volatility of volatility.

Research paper thumbnail of Inference on the Lévy measure in case of noisy observations

Statistics & Probability Letters, 2014

In this paper we are concerned with inference on the Lévy measure ν of a Lévy process in case of ... more In this paper we are concerned with inference on the Lévy measure ν of a Lévy process in case of noisy high frequency observations. It is known that standard techniques for denoising, developed for diffusion settings, do not work in this case. For this reason, we provide an extension of the pre-averaging method which allows for a consistent estimation of the Lévy distribution function even under microstructure noise. Interestingly, the asymptotic behaviour of the novel estimator is the same as in the no-noise case. This is in sharp contrast to what is known for diffusions.

Research paper thumbnail of Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps

Annals of the Institute of Statistical Mathematics, 2014

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observati... more We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable central limit theorem for the estimator by Hayashi and Yoshida (2005) in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed.

Research paper thumbnail of A note on martingale transforms for model checks

A note on martingale transforms for model checks

ABSTRACT Martingale transforms are a well known tool to derive asymptotically distribution free t... more ABSTRACT Martingale transforms are a well known tool to derive asymptotically distribution free tests for statistics based on empirical processes. Since its introduction by Khmaladze (1981) they have been frequently applied to many testing problems. In this paper martingale transforms for empirical processes are discussed from a non standard perspective with a specific focus on the case where the null hypothesis is not satisfied. For the sake of a transparent presentation we restrict our investigations to the problem of checking model assumptions in regression models, but the conclusions are generally valid. We show the weak convergence of empirical processes under fixed alternatives and introduce a new version of the martingale transform such that the transformed limiting process is a Brownian motion in scaled time, even if the null hypothesis is not satisfied.

Research paper thumbnail of Microstructure noise in the continuous case: The pre-averaging approach

Stochastic Processes and their Applications, 2009

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Limit theorems for bipower variation of semimartingales

Stochastic Processes and their Applications, 2010

This paper presents limit theorems for certain funtionals of semimartingales observed at high fre... more This paper presents limit theorems for certain funtionals of semimartingales observed at high frequency. In particular, we extend results from Jacod [4] to the case of bipower variation, showing under standard assumptions that one obtains a limiting variable, which is in general different from the case of a continuous semimartingale. In a second step a truncated version of bipower variation is constructed, which has a similar asymptotic behaviour as standard bipower variation for a continuous semimartingale and thus provides a feasible central limit theorem for the estimation of the integrated volatility even when the semimartingale exhibits jumps.

Research paper thumbnail of Bipower-type estimation in a noisy diffusion setting

Stochastic Processes and their Applications, 2009

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Understanding limit theorems for semimartingales: a short survey

Statistica Neerlandica, 2010

This paper presents a short survey on limit theorems for certain functionals of semimartingales, ... more This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We show some laws of large numbers (for the continuous and the discontinuous case) that are the most interesting from a practical point of view, and demonstrate the associated stable central limit theorems. Moreover, we state a simple sketch of the proofs and give some examples.

Research paper thumbnail of Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing

Scandinavian Journal of Statistics, 2006

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Estimation of Correlation for Continuous Semimartingales

Scandinavian Journal of Statistics, 2012

In this paper we are concerned with inference on the correlation parameter ρ of two Brownian moti... more In this paper we are concerned with inference on the correlation parameter ρ of two Brownian motions, when only high-frequency observations from two one-dimensional continuous Itô semimartingales, driven by these particular Brownian motions, are available. Estimators for ρ are constructed in two situations: Either when both components are observed (at the same time), or when only one component is observed and the other one represents its volatility process and thus has to be estimated from the data as well. In the first case it is shown that our estimator has the same asymptotic behaviour as the standard one for i.i.d. observations, whereas a feasible estimator can still be defined in the second framework, but with a slower rate of convergence.

Research paper thumbnail of Testing Semiparametric Hypotheses in Locally Stationary Processes

Scandinavian Journal of Statistics, 2013

Testing semiparametric Testing semiparametric Testing semiparametric Testing semiparametric hypot... more Testing semiparametric Testing semiparametric Testing semiparametric Testing semiparametric hypotheses in locally hypotheses in locally hypotheses in locally hypotheses in locally stationary processes stationary processes stationary processes stationary processes

Research paper thumbnail of Testing non-parametric hypotheses for stationary processes by estimating minimal distances

Journal of Time Series Analysis, 2011

Testing nonparametric Testing nonparametric Testing nonparametric Testing nonparametric hypothese... more Testing nonparametric Testing nonparametric Testing nonparametric Testing nonparametric hypotheses for stationary hypotheses for stationary hypotheses for stationary hypotheses for stationary processes by estimating processes by estimating processes by estimating processes by estimating minimal distances minimal distances minimal distances minimal distances

Research paper thumbnail of A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Journal of the American Statistical Association, 2011

A measure of stationarity in A measure of stationarity in A measure of stationarity in A measure ... more A measure of stationarity in A measure of stationarity in A measure of stationarity in A measure of stationarity in locally stationary processes locally stationary processes locally stationary processes locally stationary processes with applications to testing with applications to testing with applications to testing with applications to testing

Research paper thumbnail of The null hypothesis of (common) jumps in case of irregular and asynchronous observations

Scandinavian Journal of Statistics

This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for t... more This paper proposes novel tests for the absence of jumps in a univariate semimartingale and for the absence of common jumps in a bivariate semimartingale. Our methods rely on ratio statistics of power variations based on irregular observations, sampled at different frequencies. We develop central limit theorems for the statistics under the respective null hypotheses and apply bootstrap procedures to assess the limiting distributions. Further we define corrected statistics to improve the finite sample performance. Simulations show that the test based on our corrected statistic yields good results and even outperforms existing tests in the case of regular observations.

Research paper thumbnail of Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale

Stochastic Processes and their Applications

Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prov... more Given an Itō semimartingale with a time-homogeneous jump part observed at high frequency, we prove weak convergence of a normalized truncated empirical distribution function of the Lévy measure to a Gaussian process. In contrast to competing procedures, our estimator works for processes with a non-vanishing diffusion component and under simple assumptions on the jump process.

Research paper thumbnail of Laws of large numbers for Hayashi–Yoshida-type functionals

Finance and Stochastics

In high-frequency statistics and econometrics sums of functionals of increments of stochastic pro... more In high-frequency statistics and econometrics sums of functionals of increments of stochastic processes are commonly used and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. Inspired by the famous Hayashi-Yoshida estimator for the quadratic covariation process based on two asynchronously observed stochastic processes we investigate similar sums based on increments of two asynchronously observed stochastic processes for general functionals. We find that our results differ from corresponding results in the setting of equidistant and synchronous observations which has been well studied in the literature. Further we observe that in the setting of asynchronous observations the asymptotic behaviour is not only determined by the nature of the functional but also depends crucially on the asymptotics of the observation scheme.

Research paper thumbnail of Testing for simultaneous jumps in case of asynchronous observations

Bernoulli

This paper proposes a novel test for simultaneous jumps in a bivariate Itô semimartingale when ob... more This paper proposes a novel test for simultaneous jumps in a bivariate Itô semimartingale when observation times are asynchronous and irregular. Inference is built on a realized correlation coefficient for the jumps of the two processes which is estimated using bivariate power variations of Hayashi-Yoshida type without an additional synchronization step. An associated central limit theorem is shown whose asymptotic distribution is assessed using a bootstrap procedure. Simulations show that the test works remarkably well in comparison with the much simpler case of regular observations.

Research paper thumbnail of Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process

Bernoulli

This paper is concerned with tests for changes in the jump behaviour of a time-continuous process... more This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain tests statistics for breaks in the jump measure of an Itō semimartingale are constructed. Whenever limiting distributions depend in a complicated way on the unknown jump measure, empirical quantiles are obtained using a multiplier bootstrap scheme. An extensive simulation study shows a good performance of our tests in finite samples.

Research paper thumbnail of Nonparametric change-point analysis of volatility

The Annals of Statistics

In this work, we develop change-point methods for statistics of highfrequency data. The main inte... more In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Itô semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. Moreover, we develop methods to infer changes in the Hurst parameters of fractional volatility processes. A simulation study is conducted to demonstrate the performance of our methods in finite-sample applications.

Research paper thumbnail of A note on central limit theorems for quadratic variation in case of endogenous observation times

Electronic Journal of Statistics

This paper is concerned with a central limit theorem for quadratic variation when observations co... more This paper is concerned with a central limit theorem for quadratic variation when observations come as exit times from a regular grid. We discuss the special case of a semimartingale with deterministic characteristics and finite activity jumps in detail and illustrate technical issues in more general situations.

Research paper thumbnail of Estimation of integrated volatility of volatility with applications to goodness-of-fit testing

Bernoulli, 2015

In this paper, we are concerned with nonparametric inference on the volatility of volatility proc... more In this paper, we are concerned with nonparametric inference on the volatility of volatility process in stochastic volatility models. We construct several estimators for its integrated version in a high-frequency setting, all based on increments of spot volatility estimators. Some of those are positive by construction, others are bias corrected in order to attain the optimal rate n −1/4. Associated central limit theorems are proven which can be widely used in practice, as they are the key to essentially all tools in model validation for stochastic volatility models. As an illustration we give a brief idea on a goodness-of-fit test in order to check for a certain parametric form of volatility of volatility.

Research paper thumbnail of Inference on the Lévy measure in case of noisy observations

Statistics & Probability Letters, 2014

In this paper we are concerned with inference on the Lévy measure ν of a Lévy process in case of ... more In this paper we are concerned with inference on the Lévy measure ν of a Lévy process in case of noisy high frequency observations. It is known that standard techniques for denoising, developed for diffusion settings, do not work in this case. For this reason, we provide an extension of the pre-averaging method which allows for a consistent estimation of the Lévy distribution function even under microstructure noise. Interestingly, the asymptotic behaviour of the novel estimator is the same as in the no-noise case. This is in sharp contrast to what is known for diffusions.

Research paper thumbnail of Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps

Annals of the Institute of Statistical Mathematics, 2014

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observati... more We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable central limit theorem for the estimator by Hayashi and Yoshida (2005) in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed.

Research paper thumbnail of A note on martingale transforms for model checks

A note on martingale transforms for model checks

ABSTRACT Martingale transforms are a well known tool to derive asymptotically distribution free t... more ABSTRACT Martingale transforms are a well known tool to derive asymptotically distribution free tests for statistics based on empirical processes. Since its introduction by Khmaladze (1981) they have been frequently applied to many testing problems. In this paper martingale transforms for empirical processes are discussed from a non standard perspective with a specific focus on the case where the null hypothesis is not satisfied. For the sake of a transparent presentation we restrict our investigations to the problem of checking model assumptions in regression models, but the conclusions are generally valid. We show the weak convergence of empirical processes under fixed alternatives and introduce a new version of the martingale transform such that the transformed limiting process is a Brownian motion in scaled time, even if the null hypothesis is not satisfied.

Research paper thumbnail of Microstructure noise in the continuous case: The pre-averaging approach

Stochastic Processes and their Applications, 2009

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Limit theorems for bipower variation of semimartingales

Stochastic Processes and their Applications, 2010

This paper presents limit theorems for certain funtionals of semimartingales observed at high fre... more This paper presents limit theorems for certain funtionals of semimartingales observed at high frequency. In particular, we extend results from Jacod [4] to the case of bipower variation, showing under standard assumptions that one obtains a limiting variable, which is in general different from the case of a continuous semimartingale. In a second step a truncated version of bipower variation is constructed, which has a similar asymptotic behaviour as standard bipower variation for a continuous semimartingale and thus provides a feasible central limit theorem for the estimation of the integrated volatility even when the semimartingale exhibits jumps.

Research paper thumbnail of Bipower-type estimation in a noisy diffusion setting

Stochastic Processes and their Applications, 2009

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Understanding limit theorems for semimartingales: a short survey

Statistica Neerlandica, 2010

This paper presents a short survey on limit theorems for certain functionals of semimartingales, ... more This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We show some laws of large numbers (for the continuous and the discontinuous case) that are the most interesting from a practical point of view, and demonstrate the associated stable central limit theorems. Moreover, we state a simple sketch of the proofs and give some examples.

Research paper thumbnail of Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing

Scandinavian Journal of Statistics, 2006

Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch ge... more Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence.

Research paper thumbnail of Estimation of Correlation for Continuous Semimartingales

Scandinavian Journal of Statistics, 2012

In this paper we are concerned with inference on the correlation parameter ρ of two Brownian moti... more In this paper we are concerned with inference on the correlation parameter ρ of two Brownian motions, when only high-frequency observations from two one-dimensional continuous Itô semimartingales, driven by these particular Brownian motions, are available. Estimators for ρ are constructed in two situations: Either when both components are observed (at the same time), or when only one component is observed and the other one represents its volatility process and thus has to be estimated from the data as well. In the first case it is shown that our estimator has the same asymptotic behaviour as the standard one for i.i.d. observations, whereas a feasible estimator can still be defined in the second framework, but with a slower rate of convergence.

Research paper thumbnail of Testing Semiparametric Hypotheses in Locally Stationary Processes

Scandinavian Journal of Statistics, 2013

Testing semiparametric Testing semiparametric Testing semiparametric Testing semiparametric hypot... more Testing semiparametric Testing semiparametric Testing semiparametric Testing semiparametric hypotheses in locally hypotheses in locally hypotheses in locally hypotheses in locally stationary processes stationary processes stationary processes stationary processes

Research paper thumbnail of Testing non-parametric hypotheses for stationary processes by estimating minimal distances

Journal of Time Series Analysis, 2011

Testing nonparametric Testing nonparametric Testing nonparametric Testing nonparametric hypothese... more Testing nonparametric Testing nonparametric Testing nonparametric Testing nonparametric hypotheses for stationary hypotheses for stationary hypotheses for stationary hypotheses for stationary processes by estimating processes by estimating processes by estimating processes by estimating minimal distances minimal distances minimal distances minimal distances

Research paper thumbnail of A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Journal of the American Statistical Association, 2011

A measure of stationarity in A measure of stationarity in A measure of stationarity in A measure ... more A measure of stationarity in A measure of stationarity in A measure of stationarity in A measure of stationarity in locally stationary processes locally stationary processes locally stationary processes locally stationary processes with applications to testing with applications to testing with applications to testing with applications to testing