Concepts and definitions from the Theory of Probability, probability space, independent events and conditional probability, moment generating function and properties of moment generating functions, random vectors and joined probability distributions, marginal distributions, conditional distributions, moment generating functions of random vectors

Stochastic processes

Definition and basic concepts, description of a stochastic process, realization of a stochastic process, time heterogeneity, time dependence, conditional moments, independent and stationary process,

Some special cases of stochastic processes:  Stochastic process of white noise, Wiener (Brown Motion).

Estimation

Estimator and estimation of unknown parameters. Properties of estimators: Finite and asymptotic. Methods of estimation: Method of moments estimation, least squares estimation, maximum likelihood estimation,

Inferential Statistics

Testing hypotheses, Type I error, and type II error, level of significance. Testing hypothesis for population mean, Testing hypothesis for population variance.

This course has as prerequisite the Statistics I course. It is a more advance level course of Statistics aiming to demonstrate its important applications to Economics and Finance Theory. After being introduced to the basic concepts of Probability theory, the students are being exposed to the Stochastic Processes theory which is considered as a the cornerstone in modelling various financial variables. Next, some introductory elements from the theory of estimation and Inferential Statistics are presented useful for the Econometric course which follows.

After the completion of the course, the student

• must have understand the basic and crucial concepts of Probability and Statistics and their connection with other disciplines.
• must have a good knowledge of the Statistical methods of estimation and their use in real problems
• must be in position to select, describe and draw inferences from real data.
• must know how to use testing hypotheses and identify the statistically significant results
• will be in position to organize, apply, and monitoring a Statistical study.
• must be able to interpret financial and economical phenomena with the use of statistical tools such as stochastic processes.
• must know how to combine methods and tools for the development of statistical models in order to make decisions.

• Retrieve, analyze and synthesize data and information with the use of necessary technologies.
• Make decisions
• Work autonomously
• Work in team

Final written examination (100%)

It includes

• Multiple choice questions
• Problems

– Recommended Bibliography: 

1. Πετράκης Ανδρέας, Πετράκη Δωροθέα, Πετράκης  Λεωνιδας  (2016) Στατιστική Αυτοέκδοση Ανδρέας Πετράκης, Θεσσαλονίκη.
2. Gunder Bamberg, Franz Baur, Michael Krapp (2013) Στατιστική εκδόσεις Προπομπός, Αθήνα.
3. Μυλωνάς Νίκος (2012) Πιθανότητες και Σταιστική εκδόσει;ς Τζιόλα Θεσσαλονίκη

– Related scientific journals: