High-Frequency Statistics with Asynchronous and Irregular Data

1. Front Matter

   Pages I-XIII

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2. Theory

   1. Front Matter

      Pages 1-1

      PDF

   2. Framework

      • Ole Martin

      Pages 3-8

   3. Laws of Large Numbers

      • Ole Martin

      Pages 9-71

   4. Central Limit Theorems

      • Ole Martin

      Pages 73-109

   5. Estimating Asymptotic Laws

      • Ole Martin

      Pages 111-135

   6. Observation Schemes

      • Ole Martin

      Pages 137-153

3. Applications

   1. Front Matter

      Pages 155-155

      PDF

   2. Estimating Spot Volatility

      • Ole Martin

      Pages 157-174

   3. Estimating Quadratic Covariation

      • Ole Martin

      Pages 175-205

   4. Testing for the Presence of Jumps

      • Ole Martin

      Pages 207-240

   5. Testing for the Presence of Common Jumps

      • Ole Martin

      Pages 241-303

4. Back Matter

   Pages 305-323

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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 irregularlyobserved data.

• High-frequency statistics
• Asynchronous data
• Irregular data
• Asynchronous observations
• Random observations
• Quadratic covariation
• Test for jumps
• Test for common jumps
• Bootstrap
• Laws of large numbers
• Central limit theorems
• Bootstrapping asymptotic laws
• Random observation schemes
• Estimating quadratic covariation
• Common jumps
• quantitative finance

• Department of Mathematics, Kiel University (CAU), Kiel, Germany

  Ole Martin

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.

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