Time Series

Syllabus Details

• Unit I:(Introduction) Examples, simple descriptive techniques, trend, seasonality, the correlogram; common time series models, stationarity, moving average (MA), autoregressive (AR), ARMA and ARIMA models.
• Unit II:(Correlation Structure and Estimation) Autocovariance, autocorrelation and partial autocorrelation functions; estimation of parameters in AR, MA, ARMA and ARIMA models.
• Unit III:(Model Fitting and Forecasting) Model fitting, AIC and BIC criteria, residual analysis, testing for white noise, forecasting, Durbin-Levinson and Innovations algorithms.
• Unit IV:(Frequency Domain and State-Space Models) Inference in the frequency domain: the spectral density function, the periodogram, spectral analysis; state-space models: dynamic linear models and the Kalman filter.

Course Learning Objective

1. Explain what a time series is, what stationary processes are, and how this helps in prediction and forecasting.
2. Apply correlogram and periodogram analysis and different smoothing methods.
3. Discuss stationary time series models such as MA, AR and ARMA, and non-stationary processes with trend and ARIMA.
4. Determine the best ARMA model fitting a given time series through the AIC criterion and use it for prediction.
5. Explain volatile time series and how to model them.

Recommended Books

1. Brockwell, Peter J. and Davis, Richard A. Introduction to Time Series and Forecasting. 2nd ed. Springer, 2002
2. Brockwell, Peter J. and Davis, Richard A. Time Series: Theory and Methods. 2nd ed. Springer, 2006
3. Box, G. E. P. and Jenkins, G. M. Time Series Analysis: Forecasting and Control. 3rd ed. Prentice Hall, 1994