Course Scope

• The goal of this course is to make the students learn how to conduct empirical research in the field of finance and banking administration.
• The student will learn how to use the programming language R.
• The students will learn how to implement univariate models to time series in order to generate forecasts of the series at both short and distant prediction horizons.
• We will present the basic features and characteristics of univariate time series modeling without requiring the use of economic theory.
• The students will learn how to conduct Monte Carlo simulation experiments in order to evaluate how an estimator behaves in finite samples or how reliable is a test statistic.
• The students are introduced to the use of simulations based on the estimates of the time series models in order to achieve more accurate forecasts.
• We will show how to specify correctly a univariate time series model and how to estimate more accurately the model parameters.
• The lectures focus on the importance of stationarity, while we show how to empirically test when a series is non-stationary.
• We demonstrate how to implement the exponential smoothing and moving average methods in order to predict the future values of the data.
• The students learn how to decompose a time series among its basic components such as the trend, the seasonal and the irregular components.

Course Outline

The course offers an introduction to the Bayesian methodology employed in econometrics and statistics with increasing popularity in recent years. The Bayesian approach is applied in a Financial Economics context to tackle portfolio choice problems. We will cover the following topics.

1. Brief review of Probability Theory basics and Bayes’ rule.
2. Discussion of the contrast between the classical (frequentist) and Bayesian approaches to statistical inference and how the prior distribution combines with the likelihood to generate the posterior distribution.
3. Bayesian inference for several standard statistical distributions, such as Binomial, Normal, Poisson, and Negative-Binomial.
4. Conjugate families of prior distributions.
5. Along the way, we will address the choice of prior, with emphasis on Jeffreys’ prior, and discuss different modes of inference, that is, point estimation, interval estimation, and hypothesis testing.
6. Within the Gaussian framework, we will cover univariate linear regression models (with an application to beta estimation through shrinkage), univariate autoregressive models, multivariate linear regression models, and Vector AutoRegression models.
7. As we proceed, the course will also cover Monte Carlo simulation techniques that are used in posterior calculations, such as Acceptance-Rejection method and Gibbs sampling.
8. Applications of the Bayesian approach to portfolio choice problems. Within the Gaussian framework, we will cover the static portfolio choice problem with (a) a single risky asset and IID returns, (b) multiple risky assets and IID normal returns, (c) a single risky asset and predictable returns. Further, we will cover the Black-Litterman model from the Bayesian perspective.
9. Time permitting, we will discuss the dynamic portfolio choice problem with a single risky asset with Νormal IID returns and unknown mean and variance.

Suggested Reading

• Ηλίας Τζαβαλής, 2008. Οικονομετρία. Εκδόσεις ΟΠΑ.
• Jack Johnston, John Dinardo. Οικονομετρικές μέθοδοι. Εκδόσεις Κλειδάριθμος.
• JamesD. Hamilton. Time Series Analysis. Princeton University Press.