# 2019/20 Taught Postgraduate Module Catalogue

## MATH5802M Time Series and Spectral Analysis

### 15 creditsClass Size: 65

Module manager: Dr Haiyan Liu
Email: h.liu1@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2019/20

### Pre-requisite qualifications

MATH2715 or MATH2735.

### This module is mutually exclusive with

 MATH3802 Time Series

This module is approved as an Elective

### Module summary

In time series, measurements are made at a succession of times, and it is the dependence between measurements taken at different times which is important. The module will concentrate on techniques for model identification, parameter estimation, diagnostic checking and forecasting within the autoregressive moving average family of models and their extensions. Extensions will include transformations and differencing to deal with non-stationarity, the incorporation of seasonal dependence into the model to deal, for example with monthly series.

### Objectives

On completion of this module, students should be able to:

a) assess graphically the stationarity of a time series, including the calculation and use of a sample autocorrelation function;
b) evaluate the autocorrelation function and partial autocorrelation function for AR, MA and ARMA models;
c) use the autocorrelation and partial autocorrelation functions and other diagnostics to formulate, test and modify suitable hypotheses about time series models;
d) forecast future values of a time series;
e) develop the frequency representation of a stationary time series;
f) use the periodogram to carry out harmonic analyses;
g) use a statistical package with real data to facilitate the analysis of time series data and write a report giving and interpreting the results.

### Syllabus

1. Overview. Stationarity, outline of Box-Jenkins approach through identification of model, fitting, diagnostic checking, and forecasting. Mean, autocorrelation function, partial autocorrelation function.

2. Models. Autoregressive (AR) models, moving average (MA) models, ARMA models, their autocorrelation functions, and partial autocorrelation functions. Transformations and differencing to achieve stationarity, ARIMA models.

3. Estimation and diagnostics. Identifying possible models using autocorrelation function, and partial autocorrelation function. Estimation, outline of maximum likelihood, conditional and unconditional least squares approaches. Diagnostic checking, methods and suggestions of possible model modification.

4. Forecasting. Minimum mean square error forecast and forecast error variance, confidence intervals for forecasts, updating forecasts, other forecasting procedures.

5. Seasonality, time series regression.

6.The frequency representation of a stationary time series.

7. The use of a periodiogram to carry out harmonic analysis.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 33 1.00 33.00 Practical 1 2.00 2.00 Private study hours 115.00 Total Contact hours 35.00 Total hours (100hr per 10 credits) 150.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular example sheets and practicals.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Assignment . 20.00 Total percentage (Assessment Coursework) 20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated