This course introduces time series methodology emphasizing the data analytic aspects related to financial applications. Topics that will be discussed are as follows: Univariate linear stochastic models: ARMA and ARIMA models building and forecasting using these models. Univariate non-linear stochastic models: Stochastic variance models, ARCH processes and other non-linear univariate models. Topics in the multivariate modeling of financial time series. Applications of these techniques to finance such as time series modeling of equity returns, trading day effects and volatility estimations will be discussed.

For further information see the academic catalog: IAM526

Course Objectives

At the end of this course, the student will learn:

  • fields of application of time series in natural and social sciences
  • computation of characteristic properties of time series, such as autocorrelation and partial-autocorrelation function
  • how to construct time series models based on its characteristics
  • how to deal with non-stationary and seasonal models
  • basic concepts of heteroskedasticity and GARCH models for stochastic volatility models

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

  • distinguish stationary models from non-stationary models
  • characterise AR, MA, and ARIMA models and integrate seasonal effects in time series
  • construct and regress parsimonious models by using statistical software, such as R or MATLAB
  • build forecasting functions and recursively update forecast when new data is available
  • build ARCH and GARCH models in combination with seasonal ARIMA models

Tentative Weekly Outline

  1. Introduction: Time Series in Statistical Models
  2. Stationary Time Series
  3. Exploratory Data Analysis: Classical Regression
  4. Autoregressive (AR) Models
  5. Moving Average (MA) Models
  6. Autoregressive Moving Average (ARMA) Models
  7. Difference Equations in Time Series Context
  8. Linear Nonstationary Models: Autoregressive Integrated Moving Average (ARIMA) Models
  9. Minimum Mean Square Error Forecast
  10. Forecast Function
  11. Updating and Managing Forecast
  12. Multiplicative Seasonal Models
  13. Time Series Models of Heteroskedasticity: ARCH Models
  14. Generalised Autoregressive Conditional Heteroskedastic (GARCH) Models

Course Textbook(s)

Shumway, David S. Stoffer, Time Series Analysis and Its Applications: with R examples, Robert H., 2nd ed., 2006 George E. P. Box, Gwilym M. Jenkins, Time Series Analysis - forecasting and control, revised ed., 1976

Course Material(s) and Reading(s)

Lecture Notes will be available on ODTUClass (Moddle).

Reading(s)

  • James D. Hamilton, Time Series Analysis, 1994
  • Ruey S. Tsay, Analysis of Financial Time Series, 2nd ed., 2005

Supplementary Readings / Resources / E-Resources

Resources

Those who do not have R on their PCs can download it from the site http://www.r-project.org.

A very nice Quick-R website is located on http://www.statmethods.net.

Other

Related to the textbook, check the site http://www.stat.pitt.edu/stoffer/tsa3/R_toot.htm.