Course co-ordinator(s): Dr Fraser Daly (Edinburgh).
Aims:
This is a half course which aims to provide postgraduate students with an introductory knowledge of time series analysis, such as well known linear models, non-linear models, their probabilistic properties, estimation, model selection, statistical inference and forecasting based the fitted models, as well as their applications in insurance and finance.
Summary:
- Definitions, examples and basic concepts of time series
- Well known stationary and non-stationary linear processes, and their probabilistic properties
- Estimation, statistical inference and model selection for linear processes,
- Introduction to non-linear processes, such as ARCH and GARCH
- Introduction to processes with trend and seasonality
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Syllabus:
- Introduction: Definition and examples of time series, back-shift- and differencing-operators, strong and weak stationarity, definition of acf.
- Linear Processes: Definitions and properties of the MA(q), MA(∞), AR(p), AR(∞) and ARMA(p,q), in particualr their acf’s, causal stationarity of AR, invertibility of MA models and causal stationarity and invertibility of ARMA; concept of spectral density function and its applications; definition and properties of integrated ARIMA(p,d,q) processes; definition and properties of random walks with or without drift.
- Estimation for Linear Processes: Definitions and properties of μ, σ2, γ(k) and ρ(k); estimation of causal stationary and invertible ARMA models, in particular that of AR(p) models; model selection following the AIC and BIC; brief introduction to linear prediction and calculation of forecasting intervals for normal ARMA models; point and interval forecasts for normal random walks with or without drift.
- A Brief Introduction to Nonlinear Processes: Nonlinear properties of financial time series; definition and properties of the well known ARCH, GARCH etc.
- Time Series with Trend and Seasonality: Remove trend and seasonality using differencing operators, estimate trend and seasonality using simple moving average method, additive/multiplicative component model, forecasting by combining simple extrapolation and linear prediction.
- A brief introduction to Multivariate Time Series: Definition and properties of the VAR (vector autoregressive) model, arrange a univariate time series as a multivariate Markov model.
Learning Outcomes: Subject Mastery
At the end of studying this half course, students should be able to:
- Describe the properties of a time series using basic analytical and graphical tools.
- Understand the definitions, properties and applicabilities of well know time series models.
- Fit time series models to practical data sets and select the suitable models.
- Carry out simple statistical inference, in particular forecasting, based on the fitted models.
- Estimate and remove possible trend and seasonality in a time series.
- Analyse the residuals of a time series using stationary models.
Learning Outcomes: Personal Abilities
At the end of the course students should be able to:
- Communicate meaningfully and productively with others (including practitioners and professionals in the financial services industry) on time series analysis issues
- Demonstrate the ability to earn independently
- Manage time, work to deadlines and prioritise workloads
Reading list:
The students are referred to the following texts.
- Box, G.E.P. and Jenkins, G.M. (1976). Time Series Analysis. Holden-Day.
- Brockwell, P.J and R.A. Davis (1991). Time Series: Theory and Methods (2nd Ed.). Springer.
- Diggel, P.J. (1990). Time Series –– A biological Introduction. Oxford University Press.
- Fuller, W.A. (1996). Introduction to Time Series Analysis. John Wiley.
- Hamilton, J. D. (1994). Time Series Analysis. Prinston University Press.
Besides these the lecturer notes will be handed out. The students may also find the following (costless) web-book useful:
SCQF Level: 11.
Credits: 7.5.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.
Canvas: further information and course materials are available on Canvas