# F70TS Time Series

Course co-ordinator(s): Dr Fraser Daly (Edinburgh), Mahendran Shitan (Malaysia).

Aims:

This course aims to introduce students to, and give them the opportunity to learn about, understand, and apply, many of the fundamental concepts required for the description, modelling, and forecasting of time series data.

Summary:

• Introduction, description, and classical decomposition
• Stationary processes
• Moving average (MA) and Autoregressive (AR) processes
• ARMA and ARIMA processes
• Model building and Forecasting
• Other models used in finance and insurance

## Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisite course(s): F78PA Probability and Statistics A & F78PB Probability and Statistics B .

Location: Edinburgh, Malaysia.

Semester: 2.

Syllabus:

1. Introduction, description, and classical decomposition
• Introduction, notation, types of series, objectives of TS analysis.
• Simple models and descriptive techniques: additive and multiplicative models, trend, seasonality, cycles, noise, fits, residuals.
• Testing randomness.
• Operators.
• Describing serial dependence: autocorrelation coefficients, the sample correlation function/correlogram.
• Describing trend (smoothing): filters and moving averages, error-reducing power, effects on other components, the Slutzky-Yule effect; exponential smoothing and other methods; removing trend, differencing.
• Describing seasonality: seasonal adjustment.
2. Stationary processes
• Strict and second-order stationarity.
• Autocorrelation function/correlogram, autocovariance and autocorrelation generating functions, transform to spectrum.
• Frequency analysis, harmonic regression model, Fourier frequencies, periodogram, link with sample correlogram, estimating the process spectrum.
• General linear process, linear filters, the Lemma on acvgfs, transfer functions.
3. Moving average (MA) processes
• Properties: correlogram, generating functions, spectrum; invertibility.
• Repeated application, induced periodicity.
4. Autoregressive (AR) processes
• Properties: linear difference equations, characteristic equation, the “lambda equation”, stationarity, correlogram, Yule-Walker and Wold equations, spectrum.
5. Autoregressive moving average (ARMA) processes
• Properties: stationarity and invertibility, correlogram, spectrum.
• Extension to integrated (ARIMA) processes.
6. ARIMA processes
• Properties: three representations – difference equation, general linear process, inverted form.
• E(Y at time t+k | knowledge up to time t).
7. Model building
• Model identification: Differencing to produce stationarity. Estimating the correlogram: sampling properties of sample autocorrelation coefficients. Partial autocorrelation coefficients, estimating the partial correlation function.
• Model fitting: Estimation of parameters: least-squares, maximum likelihood. Fitted values, residuals.
• Model diagnostics: Trial overfitting; examining residuals; the principle of parsimony.
8. Forecasting
• Forecasting under fitted ARIMA models Minimum MSE forecasts (‘Box-Jenkins’ forecasting), forecast error, prediction limits, updating, eventual forecast function.
• Other forecasting techniques Extrapolation; exponential smoothing, link with B-J forecasting.
9. Other models used in financial time series (brief mention – time permitting)

Learning Outcomes: Personal Abilities

At the end of the course, students should be able to:

• Demonstrate the ability to learn independently
• Manage time work to deadlines and prioritise workloads
• Use an appropriate computer package to process data
• Present results in a way which demonstrates that they have understood the technical and broader issues of time series analysis

Reading list:

• C Chatfield, The Analysis of Time Series, 5th ed., Chapman and Hall (1996).
• Diggle, Time Series, Oxford (1990).
• Mills, Time Series Techniques for Economists, Cambridge (1990).
• Cowpertwait and Metcalfe, Introductory Time Series with R, Springer (2009).

Assessment Methods:

2-hour exam (85%) and a project (15%).

SCQF Level: 10.

Credits: 15.

## Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer

VISION: further information and course materials are available on VISION