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The aim of the course is to introduce basic theory and
methods in time series analysis and to apply them to real-life time series
to detect trends, remove seasonal components and estimate statistical
characteristics. Methods from time series analysis have applications
in a wide range of fields, including signal processing, automatic control,
econometrics, environmetrics and climatology, financial mathematics
and more.
Prerequisities:
- SF1901 or equivalent course
- SF2940 Probability Theory or equivalent course recommended
Examination:
Next written exam is Monday August 20, 2012.
Registration for this exam via
"Mina Sidor"/"My Pages"
is required. The system will be open for registration
2012-07-02 to 2012-08-05.
There will be a written exam on Thursday May 31,
2012, 14.00-19.00 hrs.
Registration for this exam via
"Mina Sidor"/"My Pages"
is required. The system will be open for registration
2012-04-23 to 2012-05-13.
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 and copy of "Formulas and survey" (without extra notes)
to the examination.
Grades are set according to the quality of the written examination.
Grades are given in the range A-F, 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.
Hand-in assignments:
There will be mandatory set of hand-in assignments.
These are applications to real data of the methods treated
during the course and some simulations. The assignments will be
handed out during one of the lectures at the beginning of the
course and will also be available through the course web pages.
There will be a deadline (TBA) 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 Monday 11 June 2012; otherwise the
whole set of assignments must be redone during
the next instance of the course.
Course literature.:
(1) P.J. Brockwell and R.A. Davis, Introduction to Time Series
and Forecasting. Springer. This book can be bought at the
Kårbokhandeln (Osquars Backe 21, on campus).
The following sections in the book are planned to be covered:
1.2-1.4, 1.5.1-1.5.2, 2.1-2.6, 3.1-3.3, 4.1-4.4, 5.1.1, 5.1.4, 5.2-5.5,
6.1, 6.3, 7.1-7.2, 7.4-7.5, 7.7, 8.1-8.5, 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"
at the Department of Mathematics, Lindstedtsvägen 25.
(3) Jan Grandell: Formulas and survey, Time series analysis.
Preliminary plan
Sections refer to textbook.
(TR = Tobias Rydén; TG = Thorbjörn Gudmundsson)
| Day |
Date |
Time |
Hall |
Topic |
Lecturer |
| Mon |
19/3 |
13-15 |
V32
|
Stationary models, autocovariance function (ACVF),
weak stationarity, AR(1), MA(1) (Sections 1.2-1.4)
|
TR |
| Tue |
20/3
|
13-15 |
V32 |
Time series decomposition, trend, seasonal component,
shift operator, difference operator,
non-negative definiteness of ACVF,
strictly stationary models, Gaussian time series
(Sections 1.5.1-1.5.2, 2.1)
|
TR
|
Thu
|
22/3
|
10-12 |
V32 |
Linear process, conditions for convergence in mean square.
causal linear processes, AR(1), MA(1),
ARMA(1,1) processes, autocovariance function and invertibility,
system polynomials
(Sections 2.2-2.3)
|
TR
|
Mon
|
26/3 |
13-15 |
V32 |
Exercises 1.1, 1.4ac, 1.8, 1.15, 2.4a
Do yourself: 1.5, 1.7, 2.1, 2.3, 3.8
|
TG
|
Tue
|
27/3 |
13-15 |
V32 |
Estimation of the mean of a stationary process,
introduction to prediction and projections (Section 2.4).
|
TR
|
Thu
|
29/3 |
10-12 |
V32 |
Prediction and projections, the Durbin-Levinson algorithm
(Section 2.5). |
TR
|
Tue
|
10/4 |
13-15 |
V32 |
The innovations algorithm for prediction,
examples (Section 2.5). |
TR
|
Thu
|
12/4 |
10-12 |
V32 |
ARMA(p,q) processes, computing their ACVF
(Sections 3.1-3.2)
|
TR
|
Mon
|
16/4 |
13-15 |
V32 |
Exercises 2.8, 3.1abc, 3.6, 3.7
Do yourself: 2.11, 2.15, 2.21, 2.22
|
TG
|
Tue
|
17/4 |
13-15 |
V32 |
The PACF for ARMA(p,q) processes,
forecasting ARMA processes (Section 3.2-3.3).
|
TR |
Th
|
19/4 |
10-12 |
V32 |
h-step prediction for ARMA processes,
Spectral density, spectral distribution and spectral
representation (Sections 3.3, 4.1)
|
TR
|
Tue
|
24/4 |
13-15 |
V32 |
The periodogram, spectral estimation
(Section 4.2)
|
TR
|
Thu
|
26/4 |
10-12 |
V32
|
Time-invariant linear filters, transfer functions,
spectral density of ARMA processes (Sections 4.3-4.4);
|
TR
|
| Fri |
27/4 |
08-10 |
V34
|
Exercises 4.4, 4.6, 4.9, 4.10
Do yourself: 4.5
| TG
|
Thu
|
3/5 |
10-12 |
V32 |
Yule-Walker estimation of AR(p) processes (Section 5.1.1)
The Hannan-Rissanen algorithm for ARMA(p,q) processes
(Section 5.1.4), ML estimation of ARMA(p,q) processes
(Section 5.2)
| TR
|
Fri
|
4/5 |
10-12 |
V34
|
Model diagnostics, forecasting, order selection
(Sections 5.3-5.5) |
TR
|
| Mon |
7/5 |
13-15 |
V32
|
ARIMA and unit root models (Sections 6.1, 6.3)
| TR
|
Tue
|
8/5 |
13-15 |
V32
|
Multivariate time series: second order
and spectral properties, multivariate ARMA processes,
cointegration
(Sections 7.1-7.2, 7.4-7.5, 7.7) |
TR
|
| Thu |
10/5 |
10-12 |
V32
|
Exercises 5.1, 5.2, 5.4
Do yourself: 5.3 |
TG
|
Mon
|
14/5 |
13-15 |
V32 |
Stochastic volatility and GARCH processes (Section 10.3.5) |
TR
|
Tue
|
15/5 |
13-15 |
V32 |
State-space models, state-space representations of
ARIMA models (Sections 8.1-8.3) |
TR
|
Mon
|
21/5 |
13-15 |
V32 |
Exercises 6.2, 6.6, 7.3, 7.5
Do yourself: 7.2 |
TG
|
Thu
|
24/5 |
13-15 |
V32 |
Kalman filtering (Section 8.4),
estimation of state-space models (Section 8.5) |
TR
|
Fri
|
25/5 |
08-10 |
V32 |
Exercises: 8.7, 8.9, 8.14, 8.15, 10.5
Do yourself: 8.8, 8.13
| TG
|
Welcome, and hope you will enjoy the course!
Tobias Rydén
To course
web page
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KTH Mathematics 
