Time Series - MAT00045H

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Additional information

Pre-requisite information: Natural Sciences students should have taken MAT00033I (Statistics Option), instead of MAT00035I.

Module will run

Occurrence	Teaching period
A	Spring Term 2022-23

Module aims

This module is to introduce a variety of statistical models for time series and cover the main methods for analysing these models. In this module students continue to develop their modelling-for-inference skills. Students learn to appreciate the difference between data indexed by time vs. cross-sectional data and the need for special exploratory and inferential techniques. This module should enrich the already acquired battery of statistical models to tackle the exploration and information extraction from real-life data with a mixture of theory and practice.

Students who wish to take this module should consider taking Stochastic Processes MAT00030H in Autumn Term, although this is not a formal pre-requisite.

The module Statistics Option (MAT00033I) can be used as a pre-requisite in place of Probability and Statistics MAT00035I if necessary.

Module learning outcomes

At the end of the course, the student should be able to define and apply the main concepts underlying the analysis of time series models. Starting with the different aspects of the concept of stationarity and exploration of real data through to fitting ARIMA models and producing forecasts. Students should also be acquainted with the concept of non-stationarity and transformations of data to stationarity. Specifically, the students should be able to:

• Compute and interpret a correlogram and a sample spectrum
• Derive the properties of ARIMA models
• Choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package
• Compute forecasts for a variety of linear models.

Module content

 

Syllabus

[ ] approximate number of lectures

1. Stationary and integrated univariate time series. Transformations to stationarity. The backwards shift operator, backwards difference operator.[3]
2. Box-Jenkins approach to time-series modelling. Autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) time series. Definition and properties. Fitting an ARIMA model to real data. [3]
3. Forecasting time series data. Simple extrapolation, model based forecasting, exponential smoothing, seasonal adjustment. [3]
4. Co-integration: Discrete random walks and random walks with normally distributed increments, both with and without drift. Multivariate autoregressive model. Co-integrated time series. [3]

5. Time series as stochastic processes. The Markov property. Univariate time series as a multivariate Markov process.[2]

6. Model identification, estimation and diagnosis of a time series. Diagnosis tests based on residual analysis. [2]

7. Applications of time series modelling to investment data. [2]

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

Chatfield, C. (2004). The analysis of time series. 6th Edition. Chapman & Hall

Brockwell P.J. and Davis R.A. (1991). Time series: theory and methods. Springer-Verlag

Harvey, A. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge University Press.