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2019 | Buch

High-Frequency Statistics with Asynchronous and Irregular Data

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Über dieses Buch

Ole Martin extends well-established techniques for the analysis of high-frequency data based on regular observations to the more general setting of asynchronous and irregular observations. Such methods are much needed in practice as real data usually comes in irregular form. In the theoretical part he develops laws of large numbers and central limit theorems as well as a new bootstrap procedure to assess asymptotic laws. The author then applies the theoretical results to estimate the quadratic covariation and to construct tests for the presence of common jumps. The simulation results show that in finite samples his methods despite the much more complex setting perform comparably well as methods based on regular data.

​About the Author:

Dr. Ole Martin completed his PhD at the Kiel University (CAU), Germany. His research focuses on high-frequency statistics for semimartingales with the aim to develop methods based on irregularly observed data.

Inhaltsverzeichnis

Frontmatter

Theory

Frontmatter
Chapter 1. Framework
Abstract
In this chapter, we specify the mathematical framework within we will derive theoretical results and develop statistical procedures.
Ole Martin
Chapter 2. Laws of Large Numbers
Abstract
In the setting of high-frequency statistics for stochastic processes, the information contained in the observed data.
Ole Martin
Chapter 3. Central Limit Theorems
Abstract
In this chapter, we will discuss central limit theorems for some of the functionals introduced in Chapter 2. Further we develop general techniques that will later in Chapters 7–9 be applied to find central limit theorems also for other more specific statistics which are based on functionals from Chapter 2.
Ole Martin
Chapter 4. Estimating Asymptotic Laws
Abstract
In order to make use of the central limit theorems 3.2 and 3.6 the law of the limiting variables.
Ole Martin
Chapter 5. Observation Schemes
Abstract
In this chapter, we discuss examples of observation schemes that yield random irregular and asynchronous observations. We will investigate their asymptotics and check whether they full the assumptions made in Chapters 2–4. I chose to collect these results in a separate chapter instead of including them in Chapters 2–4 firstly because it turns out that their proofs are rather technical and require specific arguments unrelated to the arguments in the previous chapters.
Ole Martin

Applications

Frontmatter
Chapter 6. Estimating Spot Volatility
Abstract
Our goal in this chapter is to estimate the spot volatilities σ s (1) , σ s (2) at some specific time s ∈ [0; T]. In addition to that we would like to estimate the spot correlation ρs between the two Gaussian processes C(1) and C(2). If we allow σ to be discontinuous we are additionally interested in estimating the left limits σ s– (1) , σ s– (2) s–.
Ole Martin
Chapter 7. Estimating Quadratic Covariation
Abstract
Historically the integrated volatility or realized volatility of the process X(l).
Ole Martin
Chapter 8. Testing for the Presence of Jumps
Abstract
When choosing a suitable continuous time process e.g. to model an economic or financial time series one of the first steps is to decide whether a stochastic model is sufficient that produces continuous paths or whether jumps have to be incorporated. To this end, one is faced with the problem to infer from observed data (which is usually only available at discrete time points) whether the underlying model is continuous or allows for jumps. Sometimes this problem is relatively simple to solve e.g. in the situation when very large jumps are easy to identify in a visualization of the time series data.
Ole Martin
Chapter 9. Testing for the Presence of Common Jumps
Abstract
At the beginning of Chapter 8 we discussed that when modelling a univariate process in continuous time one has to decide whether to incorporate a jump component or not. The same problem occurs in a multivariate setting where multiple processes should be modelled at once. In the situation where a multivariate model with jumps has to be specified, not only the individual jump components have to be characterized but also the dependence structure of the individual jump components has to be modelled.
Ole Martin
Backmatter
Metadaten
Titel
High-Frequency Statistics with Asynchronous and Irregular Data
verfasst von
Ole Martin
Copyright-Jahr
2019
Electronic ISBN
978-3-658-28418-3
Print ISBN
978-3-658-28417-6
DOI
https://doi.org/10.1007/978-3-658-28418-3