# MTH3260 - Statistics of stochastic processes - 2017

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Unit guides

Offered

Clayton

• Second semester 2017 (Day)

## Synopsis

Many practical experiments involve repeated measurements made over a period of time, where the individuals or systems being observed are evolving during the study period. Examples of this kind of data arise in signal processing, financial modelling and mathematical biology. For experiments of this kind, standard statistical methods that assume data points are independent and identically distributed (iid) are of limited value, due to dependencies among measurements. This unit will introduce statistical methods for such processes.

Topics: Review of fundamental statistics: their distributions, properties and limitations; Stochastic Processes: Markov, ARMA, Stationary and Diffusion Processes; Likelihood models, Graphical models, Bayesian models; Decision theory, Likelihood ratio tests, Bayesian model comparison; Sufficient statistics, Maximum Likelihood Estimation, Bayesian Estimation; Exponential families; Convergence of random variables and measures; Properties of estimators: bias, consistency, efficiency; Laws of Large Numbers and Ergodic Theorems, Central Limit Theorems; Statistics for Stationary Processes; Statistics for ARMA Processes; Statistics for Diffusion Processes

## Outcomes

On completion of this unit students will be able to:

1. Explain the central role of likelihood models in statistics
2. Construct likelihood models for stochastic processes using graphical models
3. Develop and apply likelihood ratio tests for model comparison and selection
4. Use the principle of maximum likelihood to estimate parameters of a model
5. Apply Bayesian alternatives for model comparison and estimation
6. Assess whether an estimator has desirable properties
7. Describe the asymptotic behaviour of time averages for stationary processes
8. Perform model selection and estimation tasks for stationary, ARMA and diffusion processes.

## Assessment

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• Three 1-hour lectures + One 2-hour support class + Seven hours of independent study per week

## Prerequisites

Students must be enrolled in the Master of Financial Mathematics or have passed one of the following units: MTH2222, MTH2232 or ETC2520