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M. Stat. – 504
Time Series Analysis and Forecasting
Full marks – 75
(Examination 60, Tutorial/Terminal 11.25, and Attendance 3.75)
Number of Lectures – Minimum 45
(Duration of Examination: 4 Hours)

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Aim of the Course 
The aim of this course is to get acquainted with important concepts of time series analysis and its applications.
Objectives of the Course
Students should know how to:
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Solve difference equations of a system with time series operator
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Model and forecast time series data properly
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Analyze data and signals in frequency domain and compute spectral density
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Model volatility of financial time series
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Perform multivariate time series analysis and discover interdependence
Learning outcomes
Having completing this course, students will able to do
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Apply statistical theory and methods of time series regression applicable to in economic business, environmental, geological and astrophysical problems
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Explore trends of social and economic indicators
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Estimate models for time-series data
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Interpret the results of an implemented time series analysis
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Aware of limitations and possible sources of errors in the analysis
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Present results in oral and written form

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Course Contents
Introduction: Components of time series, Stationarity, Ergodicity, White noise, Autocorrelation function, Partial autocorrelation function, Difference equations and their solution, Basic ARMA models and their extension. Box-Jenkins modeling philosophy and forecasting.
Spectral Analysis: Introduction, Fourier transformation. Periodogram, Spectral representation, Spectral density, Spectral densities for ARMA processes.
Non-stationary Time Series: Trend stationary and difference stationary time series, Integrated process, Unit roots, Unit root tests, Structural changes and their consequences, Filtering, ARIMA modeling, SARIMA modeling.
Multivariate Time Series: Structural, recursive and reduced form vector autoregressive (VAR) models, Granger causality, Impulse response functions, Forecast error variance decomposition. Spurious regression and cointegration, Tests for cointegration: Engle-Granger methodology and Johansen’s methodology, Error correction models.
Time Series Model of Heteroskedasticity: Stylized facts of financial time series. Volatility clustering, Detection of autoregressive conditional heteroskedasticity (ARCH) effects, Modeling volatility, ARCH model, Extension of ARCH model: GARCH, TARCH, GJR-GARCH, FIGARCH, EGARCH, IGARCH, PARCH, NARCH models.

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Main Books:
1)
 Andersen, T. G. and A. R. Davis (2009): Handbook of Financial Time Series, Jens-Peter Kreifs and Thomas Mikosch edition, Springer-Verlag.
2)
 Hamilton, J.D. (1994): Time Series Analysis, Princeton University Press, N.J.
3)
 Shumway, R. H. and D. S. Stoffer (2006): Time Series analysis and its Applications with R Examples.
Books Recommended:
4)
 Anderson, T.W. (1971): The Statistical Analysis of Time Series, Wiley, N.Y
5)
 Box, G.E.P. and Jenkins, G.M. (1976): Time Series Analysis: Forecasting and Control, Holden-Day, Sun Francisco.
6)
 Cryer, J. D. and K. Chan (2008): Time Series Analysis: with applications in R, 2nd Ed., Spinger, N.Y.
7)
 Findley, D.F. (1981): Applied Time Series, Vol. I, Academic press, N.Y. [Volume II]
8)
 Fuller, W.A (1976): Introduction to Statistical Time Series, Willey N.Y
9)
 Reinsel, G. C. (2003): Elements of Multivariate Time Series Analysis, Springer, N.Y.
10)
 Tsay, R. S. (2010): Analysis of Financial Time Series, Wily & Sons, N.J.