Course

Unit 1

Introduction: Examples of time series, Stationary models and autocorrelation function, Estimation and elimination of trend and seasonal components

Unit 2

Stationary Process and ARMA Models: Basic properties and linear processes, Introduction to ARMA models, properties of sample mean and autocorrelation function, Forecasting stationary time series, ARMA (p, q) processes, ACF and PACF, Forecasting of ARMA processes

Unit 3

Modeling and Forecasting with ARMA Processes: Preliminary estimation, Maximum likelihood estimation, Diagnostics, Forecasting, Order selection

Unit 4

Nonstationary and Seasonal Time Series Models: ARIMA models, Identification techniques, Unit roots in time series, Forecasting ARIMA models, Seasonal ARIMA models, Regression with ARMA errors.

Unit 5

Forecasting Techniques: The ARAR algorithm, The Holt-Winter algorithm, The Holt-Winter seasonal algorithm. Estimation of time series models.

Text Books / References

Textbooks:

1. Brockwell, Peter J. and Davis, Richard A. (2002). Introduction to Time Series and Forecasting, 2nd edition. Springer-Verlag, New York.
2. Robert H. Shumway and David S. Stoffer Time Series Analysis and Its Applications with R Examples, Springer, 2016.

References:

1. Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control, 3rd Edition, Prentice Hall, New Jersey
2. Chatfield, C. (1996). The Analysis of Time Series, 5th edition, Chapman and Hall, New York.
3. Shumway, R.H., Stoffer, D.S. (2006). Time Series Analysis and Its Applications (with R examples). Springer-Verlag, New York
4. Avishek Pal and PKS Prakash, Practical Time Series Analysis, Birmingham – Mumbai, 2017.
5. Galit Shmueli and Kenneth C. Lichtendahl Jr (2016). Practical Time Series Forecasting with R: A Hands-On Guide, 2nd Edition, Axelrod Schnall Publishers

This course introduces the fundamental concepts of time series analysis, including components, stationarity, autocorrelation, and methods for trend and seasonal decomposition. It covers modeling and forecasting using ARMA and ARIMA techniques, along with parameter estimation, diagnostics, and order selection. The course also includes seasonal models and advanced forecasting methods such as Holt-Winters and ARAR algorithms, with emphasis on practical applications in data analysis.

Course outcomes: After successful completion of the course, students will be able to:

• CO1: Understand the fundamental concepts of time series, including components, stationarity,autocorrelation, and methods for trend and seasonal decomposition.
• CO2: Apply ARMA models to analyze stationary time series and interpret ACF and PACF for modeling and forecasting.
• CO3: Estimate and validate ARMA models using techniques such as maximum likelihood estimation, diagnostic checking, and order selection.
• CO4: Analyze non-stationary time series using ARIMA and seasonal ARIMA models, including identification and forecasting methods.
• CO5: Apply advanced forecasting techniques such as Holt-Winters and ARAR algorithms for real-world time series analysis.

CO-PO Mapping