Statistics for stochastic processes 
Statistics for stochastic processes 
Academic year 2019/2020 
Course ID MAT0038 
Teachers 
Year 1st year 
Teaching period Second semester 
Type D.M. 270 TAF B  Distinctive 
Credits/Recognition 6 
Course disciplinary sector (SSD) MAT/06  probabilita' e statistica matematica 
Delivery Formal authority 
Language English 
Attendance Optional 
Type of examination Mixed 
Prerequisites Good knowledge of probability theory and the basics of stochastic processes. In more details you will need  laws of large numbers and central limit theorems  measure theory  conditional expectations  L^p spaces with respect to a probability measure  Hilbert spaces (some introductory material on this topic is present in the text books) 
Course objectivesThe goal of lectures is to introduce statistical inference for time series taking into account both the theoretical/mathematical aspects and their practical application to data analysis. Time series are considered, aiming to characterize properties, asymptotic behavior, estimations and forecasting, spectral analysis as well as decomposition in trend and seasonal components. Such concepts are applied to the analysis of simulated data or existing databases in order to infer and validate a model supporting the data. 
Results of learning outcomesKnowledge and understanding By the end of the course, the student is able to transform a real problem into a statistical one and interpret results in an effective way for phenomena evolving during the time. Moreover it is expected that the student is able to employ mathematical/statistical models for a better identification of the dependence and for forecasting the behaviour of the stochastic dynamic system under observation. Computational skills are acquired by means of the open source software R. Applying knowledge and understanding The student is requested to be able to set out statistical models in order to make evidence of relations among variable both for individual data and time series and devise appropriate computational algorithms for the models. In particular, by the end of the course, the student will know
By comparing the results obtained in performing the statistical analysis, the student has to be able to select which variables are most significant among the ones generating the experimental data, and which model better describes the dependence among the observed phenomena, when they are correlated by a temporal evolution. Communication skills The student must be able to communicate the information got from the qualitative and quantitative analysis by using the most appropriate terminology and the most useful graphical tools, aiming to avoid possible distortions, to optimize their employment and to validate the analysis. Learning skills The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of stochastic modeling of observed time series also by using the computational skills acquired in the Lab. 
Program
2. Estimation.
3. Transformation of time series.
4. ARMA models.
5. Forecasting.
6. Spectral representation of simple processes.
6. Computer lab.

Course deliveryThe course is structured in 48 hours of frontal teaching, divided into lessons of 2 hours according to academic calendar. 42 hours are of frontal lectures: during the lectures we will alternate a formal presentation of some topics, including proofs and technical details, with a more informal part where we will introduce some concepts that are useful for the analysis of data sets. Some exercises proposed by the teacher verify the practical application of the introduced topics. 6 hours are of computer lab: we will use R to simulate and analyse datasets from ARMA processes or existing databases. We refer to some particular packages useful to deal with simulations, decompositions and forecasting. Attendance is optional but recommended. The final exam will be the same for both attending and notattending students. 
Learning assessment methodsWho wants to be examined on the syllabus of the course given
For part 1. and 2. there is no pubblic mark, just an evaluation which can be: excellent, very good, good, quite good, sufficient and not sufficient sent by email through esse3.unito.it. This evaluation will be added to the oral examination mark to obtain the final mark in a proportion of 1:1. 
Support activitiesComputer lab. 
Suggested readings and bibliographyLectures in the classroom refers to
Lectures in the LAB refers to
For details on some proofs refer to
References for each topic will be made available during the lectures: for students not attending the course, a detailed summary.txt file is availabe under the webpage Teaching materials of the course. Additional materials are made available by the teacher to supplement the textbooks under the webpage Teaching materials of the course. 
Courses that borrow this teaching

Enroll Open 
Enrollment opening date 01/09/2018 at 00:00 
Enrollment closing date 30/06/2019 at 00:00 