12511 - Time Series Analysis

Learning outcomes

By the end of the course, the student should know advanced topics in non parametric time series such as estimation in the frequency domain, local polynomial regression methods, prediction. Specifically, the student should be able to estimate the signal of a time series, to estimate the (business) cycle, make a current analysis and forecast the turning points of the trend-cycle.

Course contents

Signal-noise decomposition of a time series. Local polynomial regression methods for estimating the trend. Ordinary least squares (OLS), generealised least squares (GLS), weighted least squares (WLS) estimators. Equivalence between GLS and WLS estimators. Examples: Macaulay filters, Henderson filters. Kernel estimators. Examples: Gaussian kernel, Epanechnikov kernel, beta kernels.

The problem of estimating the trend at the boundaries of the sample. Asymmetric local polynomial regression filters. Properties. Asymmetric filters applied to forecasted data. Minimum mean square revision asymmetric estimators based on different polynomial assumptions. Musgrave filters.

Inference: bias-variance trade off. Variance estimates and confidence bounds.

Frequency domain analysis: gain function and phase shift function for symmetric and asymmetric filters. Non parametric methods for spectral density estimation.

Analysis of the cycle of a time series with applications to business cycle analysis: the ideal band pass filter and Baxter-King, Hodrick-Prescott and Christiano-Fitzgerald filters.

Practical analysis in lab using MATLAB.

Readings/Bibliography

Measurements in Economics: a Handbook, Marcel Boumans Editor, Academic Press, Elsevier (chapter 16 and references therein).

Loader C. (1999), Local Regression and Likelihood, Springer, Ch. 1, 2, 9, 10.

Ruppert D., Wand, M.P., Carroll, R.J.  (2003)  Semiparametric Regression,Cambridge University Press, Ch. 3-5.

Further references will be provided during the course.

Ulteriori riferimenti bibliografici verranno segnalati durante il corso.

Teaching methods

Classroom lessons and laboratory exercises (R or MATLAB).

Assessment methods

"Analisi delle serie soriche"(Time series analysis), along with "Inferenza non parametrica" (Nonparametric inference), forms the integrated course named "Metodi non parametrici": the first module is “Inferenza non parametrica” and  starts in middle February and ends at late March, while the second part, “Analisi delle serie storiche” starts at middle April and ends at late may (they both are 5-week courses).

For the integrated course, the assessment may be based either on 2 partial exams (each one at the end of the corresponding section of the course), or on a single final exam. The aim is to check that the student has learnt the main nonparametric methods for dealing with independent/dependent observations, as well as his/her critical skills in choosing the most adequate nonparametric tool to solve a given problem.

The exam for the integrated course consists of a written exam and an oral exam. Both the written and the oral exam consist of two parts, corresponding to each of the sections of the integrated course. The overall evaluation is based on the outcome of the written and the oral exam and is expressed  in marks out of 30.

As far as the “Analisi delle serie storiche” module, every week during the course, students receive an homework which consists of theoretical questions, exercises and applications to be done with the computer. Students can decide either to do their weekly homeworks and give them to the teacher or to exercise when they like. In the former case, students have direct access to an oral exam which is a discussion of the homweork themselves (with the aim of verifying if they have really done and understood the exercises). In the latter case, students will be required to give a written examination, which essentially is a synthesis of the homework, i.e. it is made by theoretical questions, exercises or proofs and comments to a code. The written exam will be contextually discussed in an oral exam. The final mark will be assigned based on the level of preparation and consciousness of the student.

For information about the part of  (written/oral)  exam corresponding to "Inferenza non parametrica", see Guideweb at the voice "Inferenza non parametrica".

Teaching tools

Textbook, notes and papers that can be found on the institutional teacher web-site and in Alm@DL.

Links to further information

http://www2.stat.unibo.it/luati/

Office hours

See the website of Alessandra Luati