The aim of the course is to introduce basic theories and
methods in time series analysis and apply them to real life time series
to detect trends, remove seasonal components and estimate statistical
characteristics. Techniques developed in time series analysis are important
in environmental studies, biology, financial analysis, signal processing,
econometrics, etc.
Prerequisities:
 SF1901 or equivalent course
 SF2940 Probability Theory or equivalent course recommended
Examination:
There will be a written examination on Monday December 13,
2010, 14.0019.00 hrs.
Registration for the written examination via "Mina Sidor"/"My Pages"
is required.
Allowed means of assistance for the exam are a calculator (but not the
manual for it!) and the "Formulas and survey" from
Course litterature below. Each student must bring her/his own
calculator to the examination. The department will distribute the
"Formulas and survey" and it is not allowed to use your own copy.
Grades are set according to the quality of the written examination.
Grades are given in the range AF, where A is the best and F means
failed.
Fx means that you have the right to a complementary examination
(to reach the grade E).
The criteria for Fx is a grade F on the exam, and that an isolated part
of the course can be identified where you have shown a particular lack of
knowledge and that the examination after a complementary examination on
this part can be given the grade E.
Handin assignments:
There will be mandatory set of handin assignments.
These are applications to real data of the methods treated
during the course and some simulations. They are handed out during one
of the lectures at the beginning of the course or available
here and are solved in groups of
three students. Data files and mfiles for the assignments are found
here.
There is a deadline for each of the assignments. Students who do not hand
in an assignment on time are obliged to solve additional problems.
All home assignments including the additional problems if any, must be
handed in no later than the 19th of January 2011, otherwise
the whole set of assignments must be redone during the autumn 2011.
Course literature.:
(1) BD P.J.Brockwell and R.A. Davis: Introduction to Time Series
and Forecasting. SpringerVerlag. The book can be found at the
Kårbokhandeln at the adress Osquars Backe 21 at the campus.
The following sections in the book are planned to be covered:
1.21.4, 1.5.11.5.2, 2.12.6, 3.13.3, 4.14.4, 5.1.1, 5.1.4, 5.25.5,
6.1, 6.3, 7.17.2, 7.47.5, 7.7, 8.18.5, 10.3.5.
(2) Jan Grandell: Lecture notes, Time series analysis.
Contains theory that complements the textbook. Not
mandatory reading. Can be purchased at "Studentexpeditionen",
Lindstedtsvägen 25.
(3) Jan Grandell: Formulas and survey, Time series analysis.
Preliminary plan
(TR = Tobias Rydén)
Day 
Date 
Time 
Hall 
Topic 
Lecturer 
Tu 
26/10 
1012 
H1

Sections 1.21.4 in BD, stationary models,
autocovariance function (ACVF),
weak stationarity, AR(1), MA(1).

TR 
Th 
28/10

1517 
D3 
Sections 1.5.11.5.2 in BD: time series decomposition,
trend, seasonal component, shift operator, difference operator.

TR

Fr

29/10

1315 
D3 
Section 2.12.2: nonnegative definiteness of ACVF,
strictly stationary models, Gaussian time series, linear process,
conditions for convergence in mean square.
Causal linear processes, AR(1), MA(1).

TR

Mo

1/11 
1315 
E3 
Section 2.3: ARMA(1,1) processes,
autocovariance function and invertibility,
system polynomials.
Section 2.4: Estimation of the mean of a stationary process.
Introduction to prediction (Section 2.5).

TR

Th

4/11 
1517 
D3 
Introduction to prediction,
the DurbinLevinson algorithm.
(Section 2.5). 
TR

Fr

5/11 
1315 
D3 
The innovations algorithm for prediction,
examples (Section 2.5). 
TR

We

10/11 
810 
H1 
ARMA(p,q) processes, computing their ACVF
(Sections 3.13.2) 
TR

Th

11/11 
1517 
D3 
The PACF for ARMA(p,q) processes (Section 3.2)

TR

Fr

12/11 
1315 
D3 
Forecasting ARMA processes (Section 3.3).

TR

We

17/11 
812 
D3 
hstep prediction for ARMA processes (Section 3.3),
Spectral density, spectral distribution and spectral
representation (Section 4.1) 
TR 
Th

18/11 
1517 
D3 
The periodogram, spectral estimation
(Section 4.2) 
TR

Fr

19/11 
1517 
D3 
Timeinvariant linear filters, transfer functions,
spectral density of ARMA processes (Sections 4.34.4);
YuleWalker estimation of AR(p) processes (Section 5.1.1)

TR

Tu

23/11 
1012 
H1

The HannanRissanen algorithm for ARMA(p,q) processes
(Section 5.1.4), ML estimation of ARMA(p,q) processes
(Section 5.2) 
TR

Th 
25/11 
1517 
D3

Model diagnosis, forecasting, order selection
(Sections 5.35.5) 
TR

Fr

26/11 
1315 
D3 
ARIMA and unit root models (Sections 6.1, 6.3) 
TR

Th

30/11 
1012 
H1

Multivariate time series: second order
and spectral properties, multivariate ARMA processes
(Sections 7.17.2, 7.4) 
TR

Fr 
3/12 
1315 
D3

Linear prediction of random vectors (Section 7.5),
Cointegration (Section 7.7) 
TR

Tu

7/12 
1012 
H1

Stochastic volatility and GARCH processes (Section 10.3.5) 
TR

Th 
9/12 
1517 
D3

Statespace models, statespace representations of
ARIMA models (Sections 8.18.3) 
TR

Fr

10/12 
1315 
D3 
Kalman filtering (Section 8.4),
estimation of statespace models (Section 8.5)
 TR

Welcome, and hope you will enjoy the course!
Tobias Rydén
To course
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