| Unit name | Time Series Analysis |
|---|---|
| Unit code | MATH33800 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Chen |
| Open unit status | Not open |
| Pre-requisites |
Level 1 Analysis, Probability and Statistics, or Maths 1A |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Time series data are widely collected in many fields. For example in the pure sciences, medicine, marketing, economics and finance to name but a few. Time series data are different to the usual statistical data in that the observations are ordered in time and usually correlated. The emphasis is on understanding, modelling and forecasting of time-series data in both the time, frequency and time-frequency domains.
Aims
This unit provides an introduction to time series analysis mainly from the statistical point of view but also covers some mathematical and signal processing ideas.
Syllabus
(Approximate number of lectures in parentheses)
Simple descriptive techniques: times series plots; seasonal effects; trend; transformations; sample autocorrelation; the correlogram; filtering (2 lectures)
Probability models: stochastic processes; stationarity; second-order stationarity; autocorelation; white noise model; random walks; moving average processes; invertibility; autoregressive processes; Yule-Walker equations; ARMA models; ARIMA processes; the general linear process; the Wold decomposition theorem (6 lectures)
Model building: autocorrelation estimation; fitting an AR process; fitting an MA process; diagnostics (5 lectures)
Forecasting: naive procedures; exponential smoothing; Holt-Winters; Box- Jenkins forecasting; optimality models for exponential smoothing (4 lectures)
Spectral analysis: simple sinusoidal model; Wiener-Khintchine theory; the Cramer representation; periodogram analysis; relation between periodogram and autocovariance; statistical properties of the periodogram; consistent estimators of the spectral density - smoothing the periodogram (6 lectures)
Bivariate processes: cross-covariance and cross-correlation; cross-spectrum; cross-amplitude; phase spectrum; co-spectrum; quadratic-spectrum; coherence; gain (2 lectures)
ARCH modelling for econometrics. (3 lectures)
Relation to Other Units
As with units MATH 35110 (Linear Models) and 30510 (Multivariate Analysis) this course is concerned with developing statistical methodology for a particular class of problems. This course also often links to modules at Level M in Advanced Statistical Topics.
The students will be able to:
Transferable Skills:
The teaching methods consist of
30 standard lectures.
Regular problem sheets which will: develop theoretical understanding of the lectures and extra-lecture topics; relate the lectures to real practical problems arising in time-series analysis and signal processing. The students will develop a basic knowledge of time-series analysis within the R package.
Detailed solution sheets will be released approximately two weeks after the problem sheets.
Three problem sheets will count towards both assessment and credit points. It will be made clear in the lectures and on the sheets which count for assessment and credit points. Other problem sheets will be set: they will be marked but it is not compulsory to hand these in (although it would obviously be to your benefit as you would receive feedback).
The final assessment mark for Time Series Analysis will be calculated as follows:
5% from THREE satisfactory completed homework assignments. 95% from a 2½-hour written examination in April consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed. Statistical tables will be provided.
The main text will be Chatfield (see below). The lecture course will closely follow this book, but the following will also be useful:
