20236 - TIME SERIES ANALYSIS OF ECONOMIC-FINANCIAL DATA
Course taught in English
Go to class group/s: 31
Basic notions of Statistics and Probability.
The analysis of dynamic phenomena is of crucial importance in economic and financial studies. - in fact, in any field of Science. The course aims at providing solid methodological background and data-analysis skills for time series analysis, covering classical as well as modern techniques for non stationary time series, based on state-space models.
- Aims of time series analysis and descriptive techniques:
- Time series decomposition. Exponential smoothing.
- Probabilistic models for time series analysis:
- Time series as a discrete time stochastic process.
- Stationary processes. Summaries. Estimation of the autocorrelation function.
- First examples: White noise. Gaussian processes. Random walks.
- Categorical time series: Markov chains. Inference for Markov processes.
- Stationary time series: ARMA models (brief review).
- Time series with structural breaks: Hidden Markov Models.
- State space models for time series analysis:
- Motivating examples: non-stationary series; stochastic volatility; streaming data.
- State space models: definition and main properties.
- Hidden Markov models as state-space models.
- Dynamic linear models (DLM).
- Filtering, forecasting, smoothing: Kalman filter and Kalman smoother.
- Innovation process and model checking.
- Maximum likelihood estimation of unknown parameters.
- Examples for economic and financial time series. DLMs for trend, seasonality, cycle.
- Nonlinear regression by DLMs.
- ARMA models as DLMs.
- Multivariate time series (dynamic regression (example: term structure of interest rates); seemingly unrelated time series models; factor models).
- Bayesian inference and forecasting via Markov Chain Monte Carlo (MCMC).
- Recent developments.
- Explain and describe the main statistical methods for time series analysis.
- Identify the models suitable for the problems under study; estimate and make forecasts for dynamic systems, both stationary and non-stationary, with an adeguate quantification of uncertainty and risk.
- Use R for time series analysis.
- Apply and properly interpret the models and methods presented in the course in applications.
- Use adeguate statistical software (R and main R functions for time series analysis).
- Evaluate and justify their analysis on real data.
- Prepare appropriate reports of their statistical analysis in real data applications.
- Face-to-face lectures
- Online lectures
- Exercises (exercises, database, software etc.)
- Group assignments
- Online lectures: a wide set of videolectures on almost all the topics of the course - pretty close to an online, Coursera-like, course.
- Exercises: lectures in the computer room ('laboratories') on the analysis of real data - or online "video-lab". Software: R, freely available at www.r-project.org. An R-package, 'dlm', has been developed for this course.
- Students are actively involved in the learning process through individual and team work in periodic assignments.
|Continuous assessment||Partial exams||General exam|
- There are no partial exams, but there are periodic take-home assignments (individual or group work). Assigments are not mandatory, but strongly encouraged for an active learning. They are not evaluated for the final exam; yet, students who did not deliver the assignments have to answer additional questions on data-analysis with R in the written proof.
- A final project on real data analysis (individual or team work) is mandatory and evaluated for the final exam (30%).
- Written proof (70%; it can be 100% if poorly done) .
- NOTE: this structure might be slightly changed, if the need occurs, for taking into account the restrictions caused by the covid-19 pandemic.
- C. Chatfield, The Analysis of Time Series, Chapman & Hall/CRC, 2004, 6th edition (only a few chapters)
- G. Petris, S. Petrone, P. Campagnoli, Dynamic Linear Models with R, Springer, New York, 2009.
- S. Petrone Lecture notes: Introduction to Markov Chains, 2015.
- S. Petrone. Lecture notes: Hidden Markov Models
- Lecture notes, data sets, R code, RMarkdown templates etc are made available on the Bboard of the course.
- Videolectures and videolabs (online through BBoard)