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Unformatted text preview: Time Series Analysis Dr. Gavin Shaddick g.shaddick@bath.ac.uk www.bath.ac.uk/ masgs Department of Mathematical Sciences University of Bath Bath BA2 7AY 2004 1 Books Most suitable books for the course: (* Recommended) Chatfield, C. The analysis of time series. Chapman and Hall. (*) Harvey, A.C. Time series models. MIT Press. (*) Diggle, P.J. Time series; a biostatistical introduction. Oxford. Box, G.E.P. & Jenkins, G.M. Time series analysis; forecasting and control. Holden Day. Priestley, M.B. Spectral analysis and time series. Academic Press. 2 Course Outline 1. Introduction Examples; correlations. 2. Stationary Stochastic Models Stationarity; lag; autocovariance and autocorrelation functions; 3. Models for stationary time series Wold decomposition theorem, White noise; qth order moving average (MA); pth order autoregression (AR); ARMA process; invertibility; the backshift operator 4. Nonstationary processes and ARIMA models Residuals; differencing. 5. Model specification Identification; estimation of the autocorrelation function; PACF; nonstationarity; estimation; verification. 6. Forecasting MMSEP; forecasting using ARIMA models. 7. Seasonal models Seasonal MA, AR, ARMA, ARIMA 8. Structural time series models Local level model; statespace models; kalman filter 3 R For the computational elements of this course I intend this year to use a package called simply R. This package has a number of compelling advantages: (i) It is a grownup package. In fact, it is virtually identical (from the users point of view) to the wellknown package Splus; either package can be considered as the standard workplace of the modern statistician, and has builtin analytical and graphical capa bilities to handle effectively every possible statistical analysis you will ever need. If you are doing other statistical courses this year, look around in R for ways of doing the calculations of those courses. (ii) It has a full online html help browser, with search facilities. (iii) It costs nothing! Visit one of the R web sites (for example, there is one nearby at http://www.stats.bris.ac.uk/R/) to download the latest ver sion (R1.8.1). (iv) Various datasets are integral to the package, and we shall largely (though not exclusively) be using these for illustration throughout the course. As a reference for the use of R, you can print out the documentation An Intro duction to R from the web site. You can also go and look in Venables, W. N. and Ripley, B. D. Modern Applied Statistics with SPLUS (ISBN 0 387 98825 4). In the past, this course has used Minitab, which is very easy to use, but is slow and inflexible; some of the basic computations required in time series are not part of the base package, and have to be programmed separately. The use of R is via command line rather than menudriven, and while this takes a while to get used to, it is a small price to pay to get on board a package which you will use throughout your professional life....
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 Spring '09
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