Course of
Statistics of Stochastic Processes
Academic Year 2014-15
Teachers
Andrea Pugliese and Alessio Meneghetti
- Exams
- Slides of lectures
- Lecture 1 (15/9/2014). Introduction. Examples of stationary processes.
- Lecture 2 (22/9/2014). Linear processes, linear filters, MA(q) processes
- Lecture 3 (24/9/2014). Property of AVCF. Estimation of the mean
- Lecture 4 (29/9/2014). Estimation of the mean, ACVF and ACF. Introduction to prediction. In class, I was asked about a factor 4 in a formula, and I may have given a wrong answer; the correct formula for an MA(1) process is
- Lecture 5 (6/10/2014). Projection. Best linear predictor. Conditional expectation. Applications to stationary processes, in particular AR(1), MA(1); estimation of missing values.
- Lecture 6 (8/10/2014). Durbin-Levinson algorithm. Applications to AR(1), AR(p), MA(1) processe. Partial auto-correlation (PACF)
- Lecture 7 (13/10/2014). Innovations algorithm. Wold's theorem. Introduction to periodogram
- Lecture 8 (20/10/2014). Spectral density. Spectral distribution. Linear filters.
- Lecture 9 (22/10/2014). Estimation of spectral density.
- Lecture 10 (27/10/2014). Final remarks on estimation of spectral density. ARMA processes: definitions. Conditions for existence, causality and invertibility. Computing the ACVF of an ARMA process.
- Lecture 11 (3/11/2014). Computing the whole ACVF of a causal ARMA process. Spectral density of ARMA processes. Definition of ARIMA and SARIMA processes. Prediction of causal ARMA processes
- Lecture 13 (10/11/2014). Yule-Walker estimation for AR(p) processes
- Lecture 14 (17/11/2014). Estimation through fitted innovations of MA(q) and ARMA(p,q) processes. Maximum likelihood estimation for ARMA(p,q).
- Lecture 15 (19/11/2014). Comparison of different estimators and their asymptotic variance. Model choice: FPE for AR(p) processes. Kullback-Leibler discrepancy.
- Lecture 16 (24/11/2014). Estimate Kullback-Leibler discrepancy: Akaike criterion. Multivariate time series.
- Lecture 17 (1/12/2014). State space models. Kalman recursion.
- Lecture 18 (3/12/2014). Estimation in state space models. Application to a decomposition into trend and seasonal components with noise
- Lecture 19 (10/12/2014). ARCH models. Motivations, definition and first properties.
- Lecture 20 (15/12/2014). GARCH models and an application. R script used in class, and data on Standard and Poor returns 1926-1993.
- Video-audio-recording of lectures
- Exercises
- Laboratory sessions
on the use of R for time series analysis.
- Projects
- Text of the assignments.
- List of groups.
- Files for the problem A: A1, A2, A3, A4, A5, A6, A7, A8.
- Files useful for problem B: Z093.txt, Elton-Nicholson paper, FTSE, MIB, snowshoe hare, lynx tracks, measles (the CSV files have to be downloaded, not just clicked upon...).
- Data repository. Other datasets can be found in R packages, devoted to time series, in particular astsa, finTs
- Material for the course:
- Most of the course will be based on the textbook "Introduction to Time Series and Forecasting" (ITSF) by P.J. Brockwell and R.A. Davis, Springer (2002).
- The book "Time series: theory and methods" (TSTM) by P.J. Brockwell and R.A. Davis, Springer (1990) is more advanced mathematically and contains (almost) all proofs of the results in ITSF. It will serve as reference material for some topics in the course.
- "Time series Analysis and its Applications" by R. Shumway and D. Stoffer, Springer (2011) is at an intermediate level between ITSF and TSTM and can serve as an alternative approach to the subject.
- "Nonlinear Time Series" by R. Douc, E. Moulines and D.S. Stoffer, CRC Press (2014) is a recent introduction to the methods that go beyond linear analysis, the focus of the other books.
- For everything else, go to the page of previous year.
Andrea Pugliese
September 20, 2013