GRA 4153 Advanced Statistics and Alternative Data Types
GRA 4153 Advanced Statistics and Alternative Data Types
Understanding and correctly applying modern data science techniques requires a solid background in statistics. In the first part of this course we will review important concepts in probability and statistical inference to provide the required basic framework. In the second part, we will study the linear regression model (and some extensions) as well as time series analysis.
This course is in four parts:
1) - An introduction to probability
2) - The idea of statistical inference
3) - The linear regression model & extensions in the cross-sectional context
4) - The statistical analysis of time series data
In this course, we will first first review probability, the goals of statistical analysis and the basics of statistical inference. Following this we will cover regression analysis from a statistical perspective and then introduce time series and standard (ARMA) models used to analyse such data.
By the end of the course, the student:
Has a good understanding of basic probability
Is able to explain fundamental concepts in statistical inference, including estimators, tests, and the evaluation of statistical procedures
Has a good understanding of regression models from a statistical perspective.
Is able to explain fundamental time series concepts such as stationarity, auto-correlation, unit roots, persistence, and out-of-sample forecasting.
Can utilise and explain basic time series models.
Learning outcomes - Skills
By the end of the course, the student:
Can comfortably manipulate mathematical expressions involving random variables
Can utilise regression techniques to analyse cross sectional data.
Can apply basic time series modelling techniques (e.g. fitting an appropriate ARMA model) to time series data.
Can choose among, and critically evaluate, different modelling options when working with either cross - sectional or time series data.
By the end of the course, the student:
Will be able to apply basic regression and time series models and think critically about statistical inference when working with this type of data.
An introduction to probability
Probability and random variables
Expectations
Conditioning and independence
Classical limit theorems
The idea of statistical inference
The basic idea of statistical inference
Estimators, tests
Evaluation of statistical procedures
The (linear) regression model
The linear regression model
Bias/variance trade-off & Regularisation
Prediction
Generalised linear models [if time allows]
Time series data
Stationarity and autocorrelation
Fundamental time series processes
Random Walk
ARMA models
Estimation and inference
Out-of-sample forecasting
The learning activities will combine lectures (synchronous) and asynchronous learning activities. The asynchronous activities will include (i) reading provided notes and assigned materials to prepare for the lectures and (ii) solving theoretical and practical exercises (with example solutions provided afterwards). Students are expected to prepare for the lectures by reading the assigned materials, solving the assigned exercises and participate actively in the discussion of the lecture topics.
Please note that while attendance is not compulsory in all courses, it is the student’s own responsibility to obtain any information provided in class.
All parts of the assessment must be passed in order to get a grade in the course.
All courses in the Masters programme will assume that students have fulfilled the admission requirements for the programme. In addition, courses in second, third and/or fourth semester can have specific prerequisites and will assume that students have followed normal study progression. For double degree and exchange students, please note that equivalent courses are accepted.
Disclaimer
Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.
Programming in Python.
Knowledge of basic linear algebra.
| Assessments |
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Exam category: Submission Form of assessment: Submission PDF Exam/hand-in semester: First Semester Weight: 40 Grouping: Group/Individual (1 - 3) Duration: 72 Hour(s) Comment: Take home midterm exam, optionally in groups of up to 3 Exam code: GRA 41535 Grading scale: ECTS Resit: Examination when next scheduled course |
Exam category: Submission Form of assessment: Submission PDF Exam/hand-in semester: First Semester Weight: 60 Grouping: Individual Duration: 1 Week(s) Comment: Individual take home final exam Exam code: GRA 41536 Grading scale: ECTS Resit: Examination when next scheduled course |
All exams must be passed to get a grade in this course.
A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 6 ECTS credits corresponds to a workload of at least 160 hours.
