Lecture: 3 hours
Laboratory: 1 hour
Time series relationships; univariate time series models: trend, seasonality, correlated errors; regression with correlated errors; autoregressive models; autoregressive moving average models; spectral analysis: cyclical behavior and periodicity, measures of periodicity, periodogram; linear filtering; prediction of time series; transfer function models.
Prerequisite: STA 108
The nature of data collected in many different fields such as economics, biology, medicine, and engineering leads one naturally to a consideration of time series models. Samples taken from those disciplines are traditionally observed over a sequence of (equally) spaced time periods, for example, leading to monthly or yearly data. It is clear from examining the histories of such series over a number of time periods that the adjacent observations are by no means independent. Hence, the usual techniques from classical statistics, developed primarily for independent, identically distributed observations, are not applicable.
After completing the course successfully, the student should:
- Be able to recognize time dependent data and describe its important features.
- Have the prerequisite background to define, explain and use terminology such as trend, seasonality, correlated errors and periodicity.
- Be able to apply the commonly used statistical and computational time series techniques to analyze data and make inferences such as estimation and forecasts.
- Understand the statistical methodology underlying the data analysis of time series data, the most important time series models and their properties.
Summary of course contents:
This course gives an overview of the kinds of time series analyses that can arise in scientific contexts and gives examples of applications using real data. Exploratory data analysis using graphical displays and numerical summaries, such as the auto-correlation and cross-correlation functions, will be included. Students will learn how to take into account trends, seasonality, and dependent innovations, through the use of regression models with correlated errors and classical time series models such as autoregressive processes and state-space models. The representation of periodic patters with spectral analysis will be illustrated.
- Box, G.E.P., G.M. Jenkins and G.C. Reinsel (2008). Time Series Analysis, Forecasting and Control, 4th ed. Wiley, Hoboken, N.J.
- Brockwell, P.J. and R.A. Davis (1996). Introduction to Time Series and Forecasting. Springer--Verlag, New York.
- Cowpertwait, P.S.P. and A.V. Metcalfe (2009). Introductory Time Series with R. Springer--Verlag, New York.
- Shumway, R.H. and D.S. Stoffer (2010). Time Series Analysis and Its Applications, with R Examples, 3rd ed., Springer--Verlag, New York.
There is a small overlap with EEC 160 Signal Analysis and Communication, which contains some material on spectral analysis and the frequency domain.