F71TS Time Series Analysis

Dr Fraser Daly

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:

  1. Introduction: Definition and examples of time series, back-shift- and differencing-operators, strong and weak stationarity, definition of acf.
  2. 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.
  3. 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.
  4. A Brief Introduction to Nonlinear Processes: Nonlinear properties of financial time series; definition and properties of the well known ARCH, GARCH etc.
  5. 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.
  6. 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