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# Time Series - MAT00083H

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• Department: Mathematics
• Module co-ordinator: Dr. Fabio Profumo
• Credit value: 20 credits
• Credit level: H
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## Module summary

This module will teach students how to analyse time series data.

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## Module will run

Occurrence Teaching period
A Semester 2 2024-25

## Module aims

This module will teach students how to analyse time series data.

## Module learning outcomes

By 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, state space 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

1. Compute and interpret a correlogram and a sample spectrum

2. Derive the properties of ARIMA models

3. Choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package

4. Compute forecasts for a variety of linear models

5. Fit state space models and apply Kalman filter

6. Conduct spectral analysis for stationary time series.

## Module content

1. Time series as stochastic processes. The Markov property. Univariate time series as a multivariate Markov process.

2. Stationary and integrated univariate time series. Transformations to stationarity. The backwards shift operator, backwards difference operator.

3. 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.

4. Forecasting time series data. Simple extrapolation, model based forecasting, exponential smoothing , seasonal adjustment.

5. Co-integration: Discrete random walks and random walks with normally distributed increments, both with and without drift. Multivariate autoregressive model. Co-integrated time series.

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

7. The spectral density function, the periodogram, spectral analysis.

8. State-space models and Kalman filter

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Time Series
3 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Time Series
3 hours 100

## Module feedback

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