Contents - Universität Münster

Slides
Time Series Analysis
Winter Term 2015/2016
Wednesdays 14.00 – 15.30
Room: CAWM 1
Prof. Dr. Bernd Wilfling
Westfälische Wilhelms-Universität Münster
Contents
1
1.1
1.2
Introduction
Syllabus
What is Time Series Analysis?
2
2.1
2.2
Basic Concepts
Examples
Definitions
2.3
Stationarity
3
3.1
ARMA Modeling
Lag Operator
3.2
3.2.1
3.2.2
Special and Limiting Cases
MA(q) Processes
MA(∞) Processes
3.2.3
3.3
3.4
3.5
AR(q) and AR(1) Processes
Causality and Invertibility
Linear Processes and Filtering
Autocovariance Function of ARMA(p, q) Processes
4
4.1
Estimation of the Expectation and the Autocovariance Function
Ergodicity
4.2
4.3
Estimation of the Expectation
Estimation of the Autocovariance and the Autocorrelation Function
5
Partial Autocorrelation Function
5.1
5.2
Definition, Computation, Estimation
Interpretation of ACF and PACF
6
Estimation of Stationary ARMA Processes
6.1
6.2
6.3
6.4
Box-Jenkins Methodology
Estimation of ARMA(p, q) Processes
Estimation of the Lag Orders p and q
Modeling of a Stochastic Process
i
7
7.1
Integrated Processes
Stochastic Versus Deterministic Trends
7.2
7.3
7.4
7.4.1
Hypothesis Testing in AR(p) Models With Deterministic Trend
Statistical Tests for Unit Roots
Regressions With Integrated Variables
Spurious regressions
7.4.2
7.4.3
7.4.4
Cointegration
A Test for Cointegration
Vector Error Correction Models
7.4.5
Multiple Cointegration
8
8.1
Volatility Processes
Stylized Facts on the Volatility of Returns
8.2
8.3
8.4
ARCH Processes
GARCH Processes
Extensions of the GARCH Model
ii
References and Related Reading
Probability Calculus, Statistical Inference
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Mood, A.M., Graybill, F.A. and D.C. Boes (1974). Introduction to the Theory of Statistics
(3rd Edition). McGraw-Hill, Tokyo.
Mosler, K. und F. Schmid (2011). Wahrscheinlichkeitsrechnung und schließende Statistik
(4. Auflage). Springer Verlag, Heidelberg.
Wilfling, B. (2014). Advanced Statistics. Slides to the Lecture Advanced Statistics.
Winter Term 2014/2015, Westfälische Wilhelms-Universität Münster.
Time Series Analysis
Anderson, T.W. (1971). The Statistical Analysis of Time Series. Wiley and Sons, New York.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of
Econometrics 31, 307-327.
Box, G.E.P. and G.M. Jenkins (1976). Time Series Analysis: Forecasting and Control.
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Brockwell, P. and R. Davis (1991). Times Series: Theory and Methods (2nd Edition).
Springer-Verlag, New York.
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Dickey, D.A. and W.A. Fuller (1979). Distribtuion of the estimators for autoregressive time
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Dickey, D.A. and W.A. Fuller (1981). Likelihood ratio statistics for autoregressive time
series with a unit root. Econometrica 49, 1057-1072.
Ding, Z., Granger, C.W.J. and R.F. Engle (1993). A long memory property of stock market
returns and a new model. Journal of Empirical Finance 1, 83-106.
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1007.
iii
Engle, R.F. and V.K. N.G. (1993). Measuring and testing the impact of news on volatility.
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Fuller, W.A. (1976). Introduction to Statistical Time Series. Wiley and Sons, New York.
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Hamilton, J.D. (1994). Time Series Analysis. Princeton University Press, Princeton, New
Jersey.
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Berlin / Heidelberg.
MacKinnon, J.G. (1991). Critical values for cointegration tests. In: Engle, R.F., Granger,
C.W.J. (Eds.), Long-run economic relationships. Oxford University Press, Oxford,
267-276.
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Reher, G. and B. Wilfling (2016). A nesting framework for Markov-switching GARCH
modelling with an application to the German stock market. Quantitative Finance,
forthcoming.
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Schmid, F. und M. Trede (2006). Finanzmarktstatistik. Springer Verlag, Berlin Heidelberg.
Stock, J.H. and M.W. Watson (2011). Introduction to Econometrics (3rd Edition). Pearson
Education, Essex, England.
iv
Stralkowski, C.M., Wu, S.M. and R.E. DeVor (1974). Charts for the Interpretation and Estimation of the Second Order Moving Average and Mixed First Order AutoregressiveMoving Average Models, Technometrics 16, 275-285.
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Zakoı̈an, J.-M. (1994). Threshold heteroscedastic models. Journal of Economic Dynamics
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