## MATH3802 Time Series

### 10 creditsClass Size: 100

Module manager: Dr Paul Baxter
Email: P.Baxter@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

### Pre-requisite qualifications

MATH2715 or MATH2735.

### This module is mutually exclusive with

 MATH5802M Time Series and Spectral Analysis

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.

### Objectives

Objectives: To develop statistical techniques for the analysis of data collected sequentially through time.

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 on function;
b) evaluate the autocorrelation function and partial autocorrelation function for AR, MA and ARMA modes;
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) use a statistical package with real data to facilitate the analysis of the 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.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 6 1.00 6.00 Lecture 18 1.00 18.00 Practical 2 1.00 2.00 Private study hours 74.00 Total Contact hours 26.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 20.00 Total percentage (Assessment Coursework) 20.00

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

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

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