Time Series Analysis

A time series is a sequence of time-indexed observations associated with a random phenomenon, recorded in order over a period. Such series arise across econometrics and finance, engineering, medicine, genetics, sociology, and environmental science. Since observations in a time series are time-dependent, standard statistical methods are insufficient for their analysis.

Introducing both classical and contemporary approaches to time series analysis, the course covers exploratory time series analysis, stationary and non-stationary stochastic processes, ARIMA and seasonal ARIMA models (estimation and forecasting), spectral analysis, multivariate time series models, VAR models, Granger causality, impulse response functions for dynamic analysis, and volatility modelling.

This course provides a comprehensive exploration of modern time series analysis, blending classical methodologies with contemporary advancements. Participants will gain theoretical insights and practical skills to analyze and forecast time series data across diverse applications. The key topics covered include:

Exploratory Time Series Analysis, Stationary and Non-Stationary Stochastic Processes, ARIMA and Seasonal ARIMA Models – Estimation, Forecasting, Spectral Analysis of Time Series, Multivariate Time Series Models, VAR models, Granger causality and impulse response functions for dynamic analysis and Volatility modelling

AA – Apply & Analyze, U – Understand, E – Evaluate

After completion of this course, the students should be able to:

• Carry out exploratory analysis of time series data, which includes the decomposition of the time series, filtering, forecasting – U, AA, E 
• Understand the concepts of stationarity of a time series and solve the related problems - U, E 
• Test the stationarity of a given time series - U, AA 
• Understand a linear time series model and fit an appropriate linear time series model for the given data - U, AA     
• Use information criteria for the selection of appropriate time series models - U, AA 
• Understand and apply the theory related to the estimation of time series model parameters – U, AA, E 
• Do forecasting using time series models – U, AA, E 
• Solve theoretical as well as applied problems in linear time series – AA, E 

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1. Chatfield, C and Xing, H (2019). The Analysis of Time Series (7th Ed.), Chapman & Hall.
2. Cryer, J D and Chan, K-S. (2008). Time Series Analysis with Applications in R., Springer
3. Sanchez, J (2023). Time Series for Data Scientists, CU Press.
4. Shumway, R S and Stoffer, D S (2017). Time Series Analysis and Its Applications (4th Ed.), Springer.
5. Tsay, R S (2010). Analysis of Financial Time Series, 3^rd Edn., Wiley
6. Wei, W W S (2006). Time Series Analysis: Univariate and Multivariate Methods, 2nd Edition., Pearson Education.
7. Woodward, W A, Sadler, B P, and Robertson, S (2022). Time Series for Data Science, CRC Press.

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