DA 3041 Applied Time Series Analysis

Course Syllabus

Fundamental components of time series; Preliminary tests: randomness, trend, seasonality; Estimation/elimination of trend and seasonality; Mathematical formulation of time series; Stationarity concepts; Auto Covariance and Autocorrelation functions of stationary time series and its properties; Linear stationary processes and their time-domain properties: AR, MA, ARMA, seasonal, non-seasonal and mixed models; ARIMA models; Multivariate time series processes and their properties: VAR, VMA and VARMA; Parameter estimation of AR, MA, and ARMA models: LS approach, ML approach for AR, MA and ARMA models, Asymptotic distribution of MLE; Best Linear predictor and Partial autocorrelation function; Model-identification with ACF and PACF; Model order estimation techniques; Frequency domain analysis: spectral density and its properties and its estimation, Periodogram analysis.

Course Logistics

• Schedule: 5 pm - 6 pm Wednesday, 4 pm - 5 pm Thursday, 3 pm - 4 pm Friday
• Venue: 5205, Core 5.
• Teaching Assistant: Omendra Gangwar, PhD scholar, MFSDSAI, IITG

Course Evaluation

• Mid semester exam: 30%
• End semester exam: 30%
• Quizzes: 15%
• Project: 15%
• Class participation: 10%

Some references (not an exhaustive list)

• P. J. Brockwell and R.A. Davis, Introduction to Time Series and Forecasting, 2nd Edition, Springer, 2002.
• T. W. Anderson, The Statistical Analysis of Time Series. Vol. 19, 1st Edition, John Wiley & Sons, 2011.
• Rob J Hyndman and George Athanasopoulos, Forecasting: Principles and Practice (3rd ed). 2021.
• P. J. Brockwell and R.A. Davis, Time Series: Theory and Methods, 2nd Edition, Springer Science & Business Media, 2009.
• J. D. Hamilton, Time Series Analysis, 1st Edition, Princeton University Press. 2020.

Topics to be covered during the weeks