[Forside] [Hovedområder] [Perioder] [Udannelser] [Alle kurser på en side]
LEARNING OBJECTIVES:
After having followed the course the students should be able to describe and relate the features and linkages between different kinds of ARMA processes and to do calculus for specific processes using difference equation and lag operator techniques including the purpose of forecasting
· to describe likelihood based estimation and inference for AR and MA models
· to formulate the power spectrum of a time series and to interpret and derive this for specific processes. Students should formulate and interpret the power spectrum and derive this for known processes
· to formulate limit theorems for both dependent and independent processes
and to apply these to particular estimation problems
· to compare different types of non-stationary processes and to derive and
analyze their relative features
. to formulate structural dynamic time series models, and to put these on state space form
. to formulate and describe the updating equations of the Kalman Filter algorithm
· to for mulate the notion of Brownian motion, and to apply limit theorems to
derive the distribution of estimators and tests that involve unit root processes
This includes the derivation of the Dickey-Fuller distribution. The students are
expected to evaluate pitfalls in unit root testing, and to describe recently
developed unit root tests with good size and power properties
· to formulate the VAR, and to derive the properties of VAR models including
the calculation of impulse response functions
· to interpret the notion of spurious regression for integrated processes
· to define and analyze the co integrated VAR model and to derive its various
representations (The Granger representation theorem)
· to describe the VAR maximum likelihood estimation procedure for
cointegrated variables, to derive the likelihood ratio test for cointegration rank, to evaluate hypothesis testing on long-run and adjustment parameters, to formulate the identification problem for cointegrated variables, and to evaluate the role of constant and trend for the cointegration analysis.
COURSE DESCRIPTION:
The purpose of the course is to provide a rigorous
introduction to classical and modern univariate and multivariate methods in time series econometrics. A solid foundation will be given to univariate analysis of both stationary and non-stationary time series in the time and frequency domain. Box-Jenkins and forecast methods will be discussed. Asymptotic theory and limit theorems for both dependent and independent processes will be clarified. In particular, the asymptotics of non-stationary processes is presented to demonstrate the distribution theory for time series processes with unit roots. Tools and concepts for multivariate models will be presented including the vector autoregressive model for stationary and non-stationary data (the cointegrated VAR), impulse response functions, state space models and the Kalman Filter, and several other topics. The course is theoretical but will provide a solid background for undertaking thorough econometric analyses based on macroeconomic and financial time series in particular.
The course "2147: Applied Time Series and Financial Econometrics" builds upon the present course with an applied focus.
COURSE SUBJECT AREAS:
1. Difference equations and lag operators:
Hamilton , Ch. 1, 2.1-2.4, (32 pages)
2. Stationary ARMA processes
Hamilton, Ch. 3 (15 pages)
3. Forecasting
Hamilton, Ch. 4.1, 4.2, 4.7, 4.8 (24 pages)
4. Maximum likelihood estimation
Hamilton, Ch. 5.1-5.4 (12 pages)
5. Spectral analysis
Hamilton, Ch. 6 (20 pages)
6. Asymptotic distribution theory
Hamilton, Ch. 7.1, 7.2 (12 pages)
7. Non-stationary time series analysis
Hamilton, Ch. 15 (17 pages), 17.1-17.7, (30 pages),
Haldrup and Jansson (2006), pp. 252-261, (9 pages)
Haldrup (1998), 15 pages.
8. Covariance stationary VAR models
Hamilton, Ch. 10.1, 11.1, 11.2, 11.4 (20 pages)
Juselius, Ch. 3 (17 pages)
9. State Space Models and the Kalman Filter
Ericsson (2006), (22 pages)
10. Spurious regression.
Hamilton, 18.3 (3 pages)
11. The cointegrated VAR model
Specification, estimation, rank-determination, deterministics, hypothesis testing,
Juselius, Ch. 5, 6.1- 6.5, 7, 8, 10.1-10.2, 11.1-11.2 (72 pages)
12. The I(2) VAR model
Juselius, 17.1-17.3 (7 pages)
Haldrup (1998), (5 pages)
Total number of pages: 297 pages + notes and slides
REQUIRED COURSES:
3620: Econometrics and 0046: 2635: Mathematics, Dynamic Analysis.
LECTURERS: Timo Teräsvirta and Niels Haldrup.
TEACHING METHOD:
Classroom lectures with regular exercises integrated in lectures.
LITERATURE:
Ericsson, N. R., 1992: Contegration, ecoqeneity, and policy analysis: An overview
Journal of Policy Modelling, 14(3)
Haldrup, N. and M. Jansson, 2006, Improving Power and Size in Unit Root Testing, Palgrave Handbooks of Econometrics: Vol. 1 Econometric Theory, Chapter 7. T.C.
Mills and K. Patterson (eds.). Palgrave MacMillan, Basingstoke
Haldrup, N., 1998, An Econometric Analysis of I(2) Variables, Journal of Economic Surveys 12(5), pp. 595-650
Hamilton, J.D., 1994, Time Series Analysis, Princeton University Press
Juselius, K., 2006, The Cointegrated VAR model. Oxford University Press.
State Space Models and the Kalman Filter, Literature TBA
In addition, lecture notes will be distributed.
FORM OF ASSESSMENT:
20 minutes oral exam with 30 min. preparation.
EXAMINATION AIDS ALLOWED:
All - except any means of electronic communication including PCs
