[Forside] [Hovedområder] [Perioder] [Udannelser] [Alle kurser på en side]
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 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
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to formulate and relate notions of exogeneity: strict, weak, strong, and super
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to interpret the notion of spurious regression for integrated processes
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to define and analyze the cointegrated VAR model and to derive its various representations (The Granger representation theorem)
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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.
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, notions of exogeneity, 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 xxxx: Applied Time Series and Financial Econometrics builds upon the present course with an applied focus.
COURSE SUBJECT AREAS:
1. Difference equations and lag operators:
2. Stationary ARMA processes
3. Forecasting
4. Maximum likelihood estimation
5. Spectral analysis
6. Asymptotic distribution theory
7. Non-stationary time series analysis
Haldrup and Jansson (2006), pp. 252-261, (9 pages)
Haldrup (1998), 15 pages.
8. Covariance stationary VAR models
9. Notions of exogeneity in econometrics
Ericsson (2006), (22 pages)
10. Spurious regression.
11. The cointegrated VAR model
Specification, estimation, rank-determination, deterministics, hypothesis testing,
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
(Progression): 7020: Econometrics and Mathematics - Dynamic Analysis
Niels Haldrup and Timo Teräsvirta
Classroom lectures with regular exercises integrated in lectures.
English
Ericsson, N.R., 1992, Cointegration, exogeneity, 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,
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
,
Juselius, K., 2006,
The Cointegrated VAR model
.
In addition, lecture notes will be distributed.
20 minutes oral exam with 30 min. preparation.
EXAMINATION AIDS ALLOWED:
All (except any kind of electronic communication devices including PCs)
