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- Academic unit or major
- Undergraduate major in Computer Science
- Instructor(s)
- Takayasu Misako Takayasu Hideki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon1-2(WL2-201(W621)) Thr1-2(WL2-201(W621))
- Group
- -
- Course number
- CSC.T365
- Credits
- 2
- Academic year
- 2023
- Offered quarter
- 3Q
- Syllabus updated
- 2023/3/24
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course teaches the basic mathematics required for "modeling," which involves analyzing given time-series data and constructing mathematical models.
Student learning outcomes
Students will have the ability to statistically analyze time series data and build basic mathematical models that match the characteristics of the data.
Keywords
Time series, random variables, autocovariance function, information criterion, autoregressive model, state space model, Kalman filter, diffusion phenomenon, random walk
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
| ✔ Acquiring basic skills for analyzing time-series data and building mathematical models | ||||
Class flow
Lectures will be given face-to-face. For each lecture content, background and ideas will be explained and mathematical explanations will be given. The sixth and fourteenth lectures will be a summary of the previous lectures and a test will be given.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction to the lecture | Students will gain knowledge of the position and importance of time-series modeling from a broad perspective and understand the overall framework of the lecture. |
| Class 2 | Basics of Time Series Modeling 1 | Learn the basics of probability, Bayes' theorem, statistics and characteristic functions, etc. |
| Class 3 | Basics of Time Series Modeling 2 | Learn the basics of probability, Bayes' theorem, statistics and characteristic functions, etc. |
| Class 4 | Basics of Time Series Modeling 3 | Learn about the central limit theorem and the extended central limit theorem |
| Class 5 | Basics of Time Series Modeling 4 | Learn about the least squares method, the maximum likelihood method, etc. |
| Class 6 | Summary and a test | A test will be given to confirm the study up to the 5th session. |
| Class 7 | Analysis of time series data, and model selection and information criteria | Learn about stationarity, covariance relations, power spectrum, etc. |
| Class 8 | Stochastic Processes and Markov chains | Learn introductory knowledge of stochastic processes and basic properties of Markov chains |
| Class 9 | Autoregressive models 1 | Learn about the basic properties and the characteristic equation of the autoregressive model. |
| Class 10 | Autoregressive models 2 | Learn about the Yule-Walker method and related topics |
| Class 11 | State Space models and Kalman Filters | Learn the basics of state space models and Kalman filters |
| Class 12 | Random walk models and diffusion phenomena 1 | Learn the basics of diffusion phenomena from micro and macro perspectives |
| Class 13 | Random walk models and diffusion phenomena 2 | Learn the basics of random walk models |
| Class 14 | Summary and test | Summarize the 7th through 13th sessions and give a test. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None in particular.
Reference books, course materials, etc.
Genshiro Kitagawa, "Introduction of Time Series Analysis(in Japanese)"(Iwanami-shoten, 2005)
Other reference materials will be announced during the lecture. Lecture notes will be downloadable.
Assessment criteria and methods
The grade will be based on two tests (6th (40%) and 14th (60%)). Attendance will also be taken into account for overall grading.
Related courses
- CSC.T242 ： Probability Theory and Statistics
- CSC.T362 ： Numerical Analysis
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students should have basic knowledge and skills in linear algebra, calculus, and probability/statistics.
Contact information (e-mail and phone) Notice : Please replace from "[at]" to "@"(half-width character).
takayasu.m.aa[at]m.titech.ac.jp takayasu.h.aa[at]m.titech.ac.jp
045-924-5640
