Bachelor 2021/2022

Time Series and Stochastic Processes

Type: Elective course (Applied Mathematics and Information Science)

Area of studies: Applied Mathematics and Information Science

Delivered by: Department of Mathematics

Where: Faculty of Computer Science

When: 4 year, 3 module

Mode of studies: distance learning

Online hours: 10

Open to: students of one campus

Instructors: Elena R. Goryainova

Language: English

ECTS credits: 4

Contact hours: 46

Course Syllabus

Abstract

This course presents an introduction to time series analysis and stochastic processes and their applications in operations research and management science. Time series includes the description of the following models: white noise, Moving average models MA(q), Autoregressive models AR(p), Autoregressive-moving average ARMA(p,q) models, Nonlinear Autoregressive Conditional Heteroskedasticity (ARCH(p)) and Generalised Autoregressive Conditional Heteroskedasticity (GARCH(p;q)) models and VAR models. Also, the solution of the problem of identification of the ARMA process, including the model selection, estimation of the model parameters and verification of the adequacy of the selected model, is given. Methods for reducing some non-stationary time series to stationary ones by removing trend and seasonal components are described. Then, the Dolado-Jenkinson-Sosvilla-Rivero procedure is presented to distinguish non-stationary time series such as Trend-stationarity (TSP) and Difference-stationarity (DSP). The procedure for diagnosing the presence of spurious regression is also considered. Stochastic processes are discussed on a basic process Brownian motion and Poisson process. The method for constructing optimal forecasts for Gaussian stochastic processes and stationary time series is given. At the end of the course Markov chains and continuous-time Markov chains are considered. For these models, the conditions for the existence of a stationary distribution are established. In particular, are found the final distribution for the processes of «birth and death» and for the queueing system M/M/n/r.