Time Series Analysis 2400-QFU1TSA
1. Univariate time series – modeling and forecasting
- smoothing methods,
- 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)
2. 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)
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 (2005)
4. Switching models
- Markov switching models
- Threshold autoregressive models
Literature: Brooks (2008), Tsay (2005)
Type of course
Course coordinators
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.
KW01, KU01
Assessment criteria
- class presence according to common University of Warsaw rules
- preparation and presentation of own research project on real data (50%)
- written final exam (50%).
Bibliography
OBLIGATORY
Brooks, Ch. (2008/2014), Introductory Econometrics for Finance, CUP, 2nd or 3rd edition
Evans, M. K. (2003), Practical Business Forecasting, Blackwell Publishing
Tsay, R. (2010), Analysis of Financial Times Series, Wiley
Tsay, R. (2013), Multivariate Time Series Analysis: With R and Financial Applications, Wiley
Shumway, R.H. and Stoffer D.S. (2016) , Time Series Analysis and Its Applications: With R Examples, Springer, 4th edition, https://www.stat.pitt.edu/stoffer/tsa4/tsa4.pdf
SUPPLEMENTARY
Cowpertwait, Paul S.P., Metcalfe, Andrew V. (2009) Introductory Time Series With R, Springer
Cryer, J. D., & Chan, K. S. (2008), Time Series Analysis: With Applications in R, Springer
Wayne, A. and Woodward, Henry L. Gray and Alan C. Elliott (2016), Applied Time Series Analysis with R, 2nd edition, CRC Press
Shmueli, G. and Lichtendahl Jr, K.C. (2016), Practical Time Series Forecasting with R: A Hands-On Guide, 2nd edition, Axelrod Schnall Publishers Brand.
Enders, W. (2004), Applied Econometric Time Series, Wiley Series in Probability and Statistics
Kirchgässner, G. and Wolters, J. (2007), Introduction to Modern Time Series Analysis, Springer
Xekalaki, E. and Degiannakis, S. (2010) ARCH Models for Financial Applications, Wiley
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: