MATH68032 15 Semester 2 Postgraduate Taught Level 6 Jingsong Yuan Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 <p>This unit will develop further techniques of time series analysis in the time and frequency domains, for the purposes of modelling, classification and forecasting. It is suitable for students who have taken an introductory time series course. &nbsp;</p> <p>This unit will develop further techniques of time series analysis in the time and frequency domains, for the purposes of modelling, classification and forecasting. It is suitable for students who have taken an introductory time series course. &nbsp;</p> <p>The unit aims to:</p><p>Provide advanced knowledge in time series analysis and forecasting, especially in the frequency domain and for multiple time series. &nbsp;</p> <p>On successful completion of this course unit students will be able to:&nbsp;</p><ul><li>derive statistical properties of linear time series models; &nbsp;</li><li>conduct analysis in the frequency domain and use spectral methods to test stationarity and classify time series; &nbsp;</li><li>put univariate ARMA models in state space form and apply the Kalman filter for the evaluation of the Gaussian log-likelihood; &nbsp;</li><li>derive properties of ARCH/GARCH type models and use them for volatility forecasting; &nbsp;</li><li>extend univariate concepts and models to the multivariate case; &nbsp;</li><li>make forecasts using neural networks.</li></ul> <ul><li>Stationarity, autocovariance function, spectrum, linear filter, frequency response. &nbsp;</li><li>ARMA models, causality/invertibility, autocorrelation and partial autocorrelation functions. &nbsp;</li><li>ARIMA models, exponential smoothing, recursive prediction. &nbsp;</li><li>State space models, Kalman filter and its application in maximum likelihood estimation. &nbsp;</li><li>Forecasting using neural networks. &nbsp;</li><li>Spectral estimation, test of stationarity and pattern recognition. &nbsp;</li><li>ARCH and GARCH models, volatility forecasting, extended GARCH models. &nbsp;</li><li>Multiple time series, joint stationarity, cross-covariance/correlation matrix function, canonical and structural AR models, vector ARMA models.</li></ul> <p>Teaching is composed of two hours of lectures and one tutorial class per week. One week is reserved for coursework. Teaching materials will be made available online for reference and review.&nbsp;</p> 0 Other 30% 1 Written exam 70% <ul><li>Coursework: homework assignment weighting 30%.</li><li>End of semester examination: weighting 70%</li></ul> <p>Feedback tutorials will provide an opportunity for students&#39; work to be discussed and provide feedback on their understanding.&nbsp; Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.&nbsp; Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer&#39;s office hour.</p> MATH38032 Time Series Analysis Pre-Requisite Recommended MATH27720 Probability and Statistics 2 Pre-Requisite Compulsory MATH27711 Linear Regression Models Pre-Requisite Compulsory <p>Students are not permitted to take MATH48032 and MATH68032 for credit in an undergraduate programme and then a postgraduate programme.</p> N <ul><li>Priestley, M.B. (1981). Spectral Analysis and Time Series. Academic Press.</li><li>Tsay, R.S. (2013). An Introduction to Analysis of Financial Data with R. Wiley. &nbsp;</li><li>Tsay, R.S. (2013). Multivariate Time Series Analysis: With R and Financial Applications. Wiley.</li></ul> Lectures 24 Tutorials 12 0 114