Financial Econometrics

Introduction

Financial econometrics can be understood as the application of statistical techniques to data using the statistical programming language R (which is widely used in the financial industry) to answer questions in finance. Therefore, financial econometrics can be used to test theories in finance. As such, it is supports financial decision-making.

Course content

Introduction and mathematical foundations

• What is econometrics?
• Is financial econometrics different?
• Steps involved in formulating an econometric model
• Functions
• Differential calculus
• Matrices

Statistical foundations and dealing with data

• Probability and probability distributions
• A note on Bayesian versus classical statistics
• Descriptive statistics
• Types of data and data aggregation
• Simple returns vs. log returns

Review: The capital asset pricing model (CAPM) / Kapitalverdimodellen (KVM)

The classical linear regression model (CLRM)

• Regression versus correlation
• Simple regression
• Some further terminology
• The assumptions underlying the CLRM
• Properties of the OLS etsimator
• Precision and standard errors
• Statistical inference
• The t-statistic
• The exact significance level

Further development and analysis of the CLRM

• From simple to multiple linear regression
• Calculating the parameters in the generalized case
• Testing multiple hypothesis: the F-test
• Goodness of fit statistics

CLRM assumptions and the diagnostic tests

• Statistical distributions for diagnostic tests
• Assumption 1: Errors have zero mean
• Assumption 2: Errors have constant variance
• Assumption 3: Errors are linearly independent from each over time 
• Assumption 4: Errors are linearly independent from x-variables at the same point in time
• Assumption 5: Errors are normally distributed
• Multicollinearity
• Adopting the wrong functional form
• Omission of an important variable
• Inclusion of an irrelevant variable
• Parameter stability tests