Time Series Analysis

obligatory courses

Master's level course.

The lecture gives theoretical basis for time series modelling. Participants will acquire theoretical knowledge about concepts and tools used in time series analysis and forecasting. The role of practical sections is to practise econometric analysis of time series: preparing the data, estimation and post estimation procedures, model verification and diagnostics, forecasts building and evaluation. Every topic discussed during the lecture will be illustrated with case study examples and exercises to be solved by students. R software will be used - its previous knowledge is not required.

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)

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

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

- class presence according to common University of Warsaw rules

- preparation and presentation of own research project on real data (50%)

- written final exam (50%).