Time Series Analysis with SAS 1100-4_SASASC
1. Decomposition of time series and simple extrapolative models
- classical decomposition methods in additive and multiplicative form
- X12 procedure
- moving average and exponential smoothing,
- seasonal smoothing
- Holt and Holt-Winters models,
- forecasting in extrapolative models
Literature: Evans (2003)
2. Univariate time series – modeling and forecasting
- stochastic process, deterministic process and time series – definitions,
- weak and strong stationarity of time series,
- random walk (with/without drift), white noise,
- stationarity testing, unit root tests: DF/ADF, KPSS
- autocorrelation and partial autocorrelation functions, correlograms,
- autoregressive process AR(p) and its features,
- moving average process MA(q) and its characteristics,
- ARMA(p,q) models, stationarity conditions, Box-Jenkins procedure, information criteria AIC, SBC (BIC), parameter estimation and model diagnostics,
- Portmanteau test, Box-Pierce and Ljung-Box tests,
- integrated series, integration level, differentiation of series,
- ARIMA models for integrated series,
- forecasting in ARMA/ARIMA models, ex-ante forecast error, confidence intervals for the forecast, ex-post measures of forecast quality (absolute and percentage)
- seasonal SARIMA models – estimation and forecasting,
Literature: Brooks (2008), Charemza, Deadman (1997), Enders (2004)
3. Modeling volatility
- stylised facts in financial time series, leptokurtic series, “fat tails”, leverage effect,
- homoskedasticity vs. heteroskedasticity,
- conditional vs. unconditional variance,
- ARCH(q) process and its features, testing for conditional heteroskedasticity,
- estimation of ARCH models,
- generalized ARCH models (GARCH), estimation methods,
- GARCH extensions: IGARCH, GARCH-M, GARCH-t, asymmetric GARCH models: EGARCH, GJR-GARCH, TGARCH
Literature: Brooks (2008), Enders (1995), Mills (1999), Tsay (2002)
4. Multivariate time series models
- long-term relationships in financial time series
- cointegration – definition and testing, estimation of cointegrating vector, Johansen test, error correction mechanism models (ECM),
- Granger causality testing,
- vector autoregression models (VAR),
- impulse response functions,
- variance decomposition,
- vector error correction mechanism models (VECM),
Literature: Brooks (2008), Enders (1995), Charemza, Deadman (1997)
5. Switching models
- Markov switching models
- Threshold autoregressive models
Learning outcomes
Students will be able to identify features of time series and select best modeling method. They will know how to decompose time series into its components, identify, estimate and interpret models in univariate and multivariate time series framework (for macroeconomic and financial data), produce and evaluate forecasts and verify research hypotheses. In addition, students will know how to apply wide range of models, including modeling non-stationary time series and long-run relationships between economic variables.
Assessment criteria
Course assesment will be based on students' own projects prepared in at most 2-person groups. The project will require model estimation and generating out-of-sample forecasts for four time series selected by students. The aim of the project will the comparison of forecast quality for extrapolative Holt/Holt-Winters models and ARIMA/SARIMA models. Alternative (more advanced) projects are also possible upon agreement with the lecturers.
Bibliography
1. SAS, OnlineDoc
2. Box, G. E. and G. M. Jenkins (1994) Time Series Analysis, Prentice Hall. Brockwell,
3. P. J. and R. A. Davis (1996) Introduction to Time Series and Forecasting, Springer-Verlag.
4. Evans,M.K. (2003) Practical Business Forecasting, Blackwell Publishing.
5. Gouriéroux, C. (1997) ARCH Models and Financial Applications, Springer-Verlag
6. Gourieroux,C., Jasiak, J. (2001) Financial Econometrics: Problems, Models, and Methods, Princeton University Press
7. Hamilton, James D. (1994) Time Series Analysis, Princeton University Press.
8. Judge G. G., W. E. Griffiths, R. C. Hill, H. Lütkepohl and T. C. Lee (1985) The Theory and Practice of Econometrics, John Wiley & Sons, Inc., New York.
9. Maddala, G.S. (2006) Ekonometria, PWN, Warszawa
10. Tsay, R. S. (2002) Analysis of Financial Time Series, Wiley
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: