STATF507
Tuesday 9h00-13h00
Location: S.R42.4.110
This course is a continuation of Time Series 1, which I have taught the last summer semester.
The main objectives are to cover some classical (standard) time series topics, which we were
not able to cover in TSI and to give some detailed asymptotics theory for stationary data. Specifically this comprises the (1) Wold decomposition and the study
of the time series (2) in the frequencey domain. Then I would like prove the (3) ergodic theorem, which can be viewed as the law of large numbers
for stationary data,
and a version of the (4) central limit theorem for stationary processes. With these results at
hand we have a closer look at the (5) asymptotics of serval estimators in the ARMA context (mean,
ACF and parameters). Finally we will introduce the (6) GARCH model, as a very important example
for a non-linear process. After studying basic properties, we will derive (7) the quasi-maximum
likelihood estimators, and study their properties in detail.
Literature
Brockwell and Davis (1991). Time Series: Theory and Methods. Springer.
Billingsley (1999). Convergence of Probability Measures. Wiley.
Billingsley (1995). Probability and Measure. Wiley.
Hamilton (1994). Time Series Analysis. Princeton University Press.
Franq and Zakoian (2009). Modèles GARCH. Economica.
Lecture notes
I will write chapter by chapter, here is the current version (the new material starts at Chapter 6):
Lecture Notes
Updated: Nov 14 2011