Blanka Sedivá

Mathematical Models in Econometrics KMA/MME

winter semester 2017-2018

Blanka Sedivá, Západočeská univerzita v Plzni (timetable)

Information in the system STAG portal.zcu.cz

Dates of lectures: 26.9.2017, 10.10.2017, 24.10.2017, 7.11.2017, 21.11.2017, 5.12.2017

Module outline (PDF)
Elements of Assessment During the semester students will be assigned tasks and by completing them, they could be awarded at most 5 points. Acquired points will be accounted for the final exam assessment.

Exam Requirements The exam itself consists of theoretical and practical part. The theoretical part of the exam is written and is mainly focused on knowledge of the fundamental concepts and methods of econometrical modelling. Succeeding in the theoretical part is the necessary condition to entry the practical part of the exam. In the practical part students shall demonstrate usage of mathematical software of their choice within the given task. The crucial element is to be able to correctly interpret acquired results and to show overall understanding of the discussed topic.
Exam Assessment:
- Points acquired during the semester - the maximum is 5 points; the necessary minimum is 3 points.
- The theoretical part (written test) - the maximum is 10 points; the necessary minimum is 6 points.
  !!Hand written notes in range of A5 page could be used during the test!!
- The practical part - the maximum is 10 points; the necessary minimum is 6 points. Assessment of the practical part also includes the oral examination during which students are supposed to demonstrate understanding of the topic and to interpret the acquired results.

Module outline and Materials
- 1. topic Classical Linear Regression Model.
  The Structure of Econometrics Data, The Simple Linear Model, The Ordinary Least Squar.
  presentation01
  Statisticalproperties of the simple linear regression model.
  presentation02
  
  Regression model in matrix form. Statistical properties of the ordinary least square estimators. Evaluation of the regression model. Testing statistical significance of the regression model and testing statistical significance of individual parameters. Choice of appropriate model.
  presentation03
  presentation04
  presentation05
- Assessment 1:
  Using numerical experiments, verify the basic statistical properties of the classical and classical normal linear regression model estimates given in the Gauss-Mark theorem.
- 2. topic Linear Regression Model with Inconstant Covariation Matrix
  
  Regression diagnostics, different types of residuals and their properties, identification of outliers.
  presentation06
  Problems connected with violating of linear regression assumptions (i.e. heteroscedasticity, autocorrelation and multicollinearity).
  presentation07
  presentation08
  presentation09
- Assessment 2:
  Find a suitable economic or financial data, perform a linear regression and find your model residuals. Detect outliers, leverage points and points of high influence using residuals with known distribution, hat matrix and various measures of influence. Try to find more suitable model for the data in terms of the regression function and/or additional explanatory variables using selected quality criterions. Then test your final model for the presence of autocorrelation, heteroscedasticity and multicollinearity. Comment your findings and eventually suggest possible remedies.
  
  Regression models with dummy variables. Mixed regression models.
  
  Regression models with autoregressive residuals and lagged regression.
- 3. topic Generalised Linear Regression Models.
  
  Discrete and restricted explanatory variable. Probit and logit regression and its usage. Censored explanatory variable.
  presentation10
  Generalised linear (GLM) models.
  presentation11
- Assessment 3:
  Choose a discrete explained variable dataset below or find your own suitable dataset and perform an appropriate type of regression (e.g. logit, probit, Poisson, etc.). Write a short documentation where you describe the data and comment your findings.