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Ogihara Lab
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The lab uses statistics to capture phenomena that change randomly and applies the results to the analysis of financial data.
AboutAbout the lab
Reading random movements through statistics
The Ogihara Lab studies the statistical analysis of stochastic processes and its application to financial data.
A stochastic process is a mathematical representation of a phenomenon that changes randomly over time.
The lab models high-frequency data, which records every stock trade, with stochastic processes and analyzes data from the Tokyo Stock Exchange.
The lab also works on training stock price models with neural networks and on predicting the arrival of buy and sell orders.
Key terms
- Stochastic process
- A mathematical model of a quantity that changes randomly over time. It is used for things such as stock price movements.
- High-frequency data
- Data recorded at very fine time intervals, such as every stock trade made during a single day.
- Stochastic differential equation
- An equation that describes change that includes random fluctuations. It is used as a model of stock prices.
ResearchResearch themes
The lab studies parametric and nonparametric estimation methods for stochastic processes, along with their theoretical properties. As applications to financial data, it works on stock price models for high-frequency data and on modeling buy and sell order information (the order book).
*Illustrative imageStatistical Analysis of High-Frequency Data
High-frequency data contains a great deal of information, but it is difficult to analyze because observation times do not align across stocks (asynchronous observation) and the observations contain noise. The lab studies methods that account for this observational structure to estimate quantities such as variance and covariance.
*Illustrative imageModeling Stock Prices with Neural Networks
The lab uses neural networks to learn the various characteristics of the stock price models underlying high-frequency data from vast amounts of data. The coefficients of a stochastic differential equation are represented by neural networks, and models of stock price movements are learned through maximum-likelihood-type estimation.
*Illustrative imagePoint Process Modeling of the Order Book
The lab models buy and sell orders placed before trades are executed (the order book) with the Hawkes process, a self-exciting point process, and investigates how stock prices are formed. This also leads to predicting the arrival of future orders and to finding optimal strategies for splitting orders when trading large quantities of stock.
*Illustrative imageTheoretical Optimality of Estimation
The lab studies local asymptotic mixed normality (LAMN), which is important for discussing whether an estimation method is optimal. For statistical models of stochastic differential equations, it uses Malliavin calculus, a calculus for Brownian motion, to examine the behavior of the likelihood function.
MembersFaculty
- Associate ProfessorTeppei OgiharaPublications ↗
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Market centre in Tokyo stock exchange” ehnmark / CC BY 2.0 (cropped)
- Statistical Analysis of High-Frequency Data: “SamplePathsDiffusionProcess” Jbusemey / CC0 (cropped)
- Modeling Stock Prices with Neural Networks: “Artificial Neural Network Example” Jhedengren / CC BY-SA 4.0 (cropped)
- Point Process Modeling of the Order Book: “Order Book, depth of market” RuppaZakir / CC BY-SA 4.0 (cropped)
- Theoretical Optimality of Estimation: “Wiener process 3d” Sullivan.t.j / CC BY-SA 3.0 (cropped)
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