Course

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

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

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

Text Books:

1. Brockwell, Peter and Davis, Richard A. (2002). Introduction to Time Series and Forecasting, 2nd edition. Springer-Verlag, New York.

1. 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,3rdEdition,PrenticeHall,New
2. Chatfield, C. (1996). The Analysis of Time Series, 5th edition, Chapman and Hall, New
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. Galit Shmueli and Kenneth Lichtendahl Jr (2016). Practical Time Series Forecasting with R: A Hands- On Guide, 2nd Edition, Axelrod Schnall