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Unit of study_

STAT3925: Time Series (Advanced)

This unit will study basic concepts and methods of time series analysis applicable in many real world problems applicable in numerous fields, including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. This unit will investigate the basic methods of modelling and analyzing of time series data (ie. Data containing serially dependence structure). This can be achieved through learning standard time series procedures on identification of components, autocorrelations, partial autocorrelations and their sampling properties. After setting up these basics, students will learn the theory of stationary univariate time series models including ARMA, ARIMA and SARIMA and their properties. Then the identification, estimation, diagnostic model checking, decision making and forecasting methods based on these models will be developed with applications. The spectral theory of time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows will be studied in detail. Further, the methods of analyzing long memory and time series and heteroscedastic time series models including ARCH, GARCH, ACD, SCD and SV models from financial econometrics and the analysis of vector ARIMA models will be developed with applications. By completing this unit, students will develop the essential basis for further studies, such as financial econometrics and financial time series. The skills gain through this unit of study will form a strong foundation to work in a financial industry or in a related research organization.

Code STAT3925
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
STAT2X11 and (MATH1X03 or MATH1907 or MATH1X23 or MATH1933)

At the completion of this unit, you should be able to:

  • LO1. 1.Explain and examine time series data and identify components of a time series; remove trends, seasonal and other components.
  • LO2. Identify stationarity time series; sample autocorrelations and partial autocorrelations, probability models for stationary time series.
  • LO3. Explain homogeneous nonstationary time series, simple and integrated models and related results.
  • LO4. Apply estimation and fitting methods for ARIMA models via MM and MLE methods.
  • LO5. Apply hypothesis testing, diagnostic checking and goodness-of-fit tests methodology.
  • LO6. Construct forecasting methods for ARIMA models.
  • LO7. Explain spectral methods in time series analysis.
  • LO8. Apply financial time series and related models to straightforward problems.
  • LO9. Apply the methods of analysis of GARCH and other models for volatility.
  • LO10. Explain and apply methods of vector time series models