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ITSM for Windows: A User’s Guide to Time Series Modelling and Forecasting PDF

126 Pages·1994·6.057 MB·English
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ITSM for Windows A User's Guide to Time Series Modelling and Forecasting Peter J. Brockwell Richard A. Davis ITSM for Windows A User's Guide to Time Series Modelling and Forecasting With 63 Illustrations and 2 Diskettes Written in collaboration with Rob J. Hyndman Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Peter J. Brockwell Mathematics Departmenl Royal Melbourne Institute of Technology Melbourne, Victoria 3001 Australia Richard A. Davis Department of Statistics Colorado State University Fort Collins, CO 80523 USA Library of Congress Cataloging in Publication Data applied for. Printed on acid-free paper. © 1994 Springer·Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer.Veriag New York, Inc., 17S Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information -storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereaf· ter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign thaI such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Ellen Seham; manufacturing supervised by Jacqui Ashri. Photocomposed copy prepared from the author's LaTeX files. 9876S432J Additional material to this book can be do,,-nloaded from http://extras.springer.com. ISBN-13: 978·0-387-94337-4 c-ISBN·13: 978·1·4612·2676-5 001: 10 .1 007/978-1-4612-2676-5 Preface The package ITSM (Interactive Time Series Modelling) evolved from the programs for the IBM PC written to accompany our book, Time Series : Theory and Methods, published by Springer-Verlag. It owes its existence to the many suggestions for improvements received from users of the earlier programs. Since the release of ITSM Version 3.0 in 1991, a large number of further improvements have been made and incorporated into the new ver sions, ITSM41 and ITSM50 , both of which are included with this package. The latter is capable of handling longer series but requires a PC 80386 or later with 8 Mbytes of RAM and an EGA or VGA card. The earlier version ITSM41 requires only a PC 80286 or later with EGA or VGA. (For precise system requirements, see Section 1.2 on page 2.) The main new features of the programs are summarized below. • Addition of two new modules, BURG and LONGMEM for multivariate and long-memory modelling respectively; • Adaptation of the programs to run either under DOS or under Mi crosoft Windows (Version 3.1 or later); • An extremely easy to use menu system in which selections can be made either with arrow-keys, hot-keys or mouse; • Development of Version 5.0 which permits the analysis of univariate series of length up to 20,000 and multivariate series of length up to 10,000 with as many as 11 components (on computers with 8Mb of RAM); • Incorporation into the program PEST of a number of new features in cluding Hannan-Rissanen estimation of mixed ARMA models, Ljung Box and McLeod-Li diagnostic statistics, automatic AleC minimiza tion for Yule-Walker and Burg AR models and superposition of the graphs of sample and model spectra and autocovariance functions; • Incorporation into SMOOTH of a frequency-based smoother (which eliminates high-frequency components from the Fourier transform of the data) and automatic selection of the parameter for exponential smoothing; vi Preface • Addition of new features (described in Appendix A) to the screen editor WORD6. The package includes the screen editor WORD6 and eight programs, PEST, SMOOTH, SPEC, TRANS, ARVEC, BURG, ARARand LONGMEM, whose functions are summarized in Chapter 1. If you choose to install the smaller version, ITSM41, the corresponding programs PEST, SPEC and SMOOTH can deal with time series of up to 2300 observations and ARVEC, BURG, ARAR, LONGMEM and TRANS can handle series of lengths 700, 700, 1000, 1000 and 800 respectively. If your PC meets the system requirements, you should load I TSM50, which can handle much longer series (20,000 univariate or 10,000 multivariate observations) . We are greatly indebted to many people associated with the develop ment of the programs and manual. Outstanding contributions were made by Joe Mandarino, the architect of the original version of PEST, Rob Hynd man, who wrote the original version of the manual for PEST, and Anthony Brockwell, who has given us constant support in all things computational, providing WORD6, the graphics subroutines, the current menu system and the expertise which made possible the development of Version 5.0. The first version of the PEST manual was prepared for use in a short course given by the Key Centre in Statistical Sciences at Royal Melbourne Institute of Technology (RMIT) and The University of Melbourne. We are indebted to the Key Centre for support and for permission to make use of that mate rial. We also wish to thank the National Science Foundation for support of the research on which many of the algorithms are based, R. Schnabel of the University of Colorado computer science department for permission to use his optimization program, and Carolyn Cook for her assistance in the final preparation of an earlier version of the manual. We are grateful for the encouragement provided by Duane Boes and the excellent working environments of Colorado State University, The University of Melbourne and RMIT. The editors of Springer-Verlag have been a constant source of support and encouragement and our families, as always, have played a key role in maintaining our sanity. Melbourne, Victoria P.J. Brockwell Fort Collins, Colorado R.A. Davis February, 1994 Contents Preface v 1 Introduction 1 1.1 The Programs . 1 1.2 System Requirements 2 1.2.1 Installation .. 3 1.2.2 Running ITSM 7 1.2.3 Printing Graphs 7 1.3 Creating Data Files 8 2 PEST 9 2.1 Getting Started . 9 2.1.1 Running PEST 9 2.1.2 PEST Thtorial 10 2.2 Preparing Your Data for Modelling . 10 2.2.1 Entering Data 11 2.2.2 Filing Data . . . . . 12 2.2.3 Plotting Data . . . . 12 2.2.4 Transforming Data . 13 2.3 Finding a Model for Your Data 19 2.3.1 The ACF and PACF .. 19 2.3.2 Entering a Model . . . . 21 2.3.3 Preliminary Parameter Estimation 22 2.3.4 The AICC Statistic ........ 24 2.3.5 Changing Your Model ....... 26 2.3.6 Parameter Estimation; the Gaussian Likelihood . 27 2.3.7 Optimization Results . 31 2.4 Testing Your Model ......... 34 2.4.1 Plotting the Residuals . . . . 36 2.4.2 ACF /PACF of the Residuals 36 2.4.3 Testing for Randomness of the Residuals . 37 2.5 Prediction . . . . . . . . 41 2.5.1 Forecast Criteria . . . . . . . . . . . . . . 41 viii Contents 2.5.2 Forecast Results 41 2.5.3 Inverting Transformations . . . . . . . . . . . . . . . 42 2.6 Model Properties . . . . . . . . . . . . . . . . . . . . . . . . 44 2.6.1 ARMA Models . . . . . . . . . . . . . . . . . . . . . 45 2.6.2 Model ACF, PACF .................. . 46 2.6.3 Model Representations . . . . . . . . . . . . . . . . . 47 2.6.4 Generating Realizations of a Random Series .... . 49 2.6.5 Model Spectral Density ............... . 50 2.7 Nonparametric Spectral Estimation. . . . . . . . . . . . . . 53 2.7.1 Plotting the Periodogram .............. . 53 2.7.2 Plotting the Cumulative Periodogram ....... . 55 2.7.3 Fisher's Test ..................... . 56 2.7.4 Smoothing to Estimate the Spectral Density ... . 57 3 SMOOTH 60 3.1 Introduction .......................... . 60 3.2 Moving Average Smoothing ................. . 61 3.3 Exponential Smoothing ................... . 62 3.4 Removing High Frequency Components .......... . 64 4 SPEC 66 4.1 Introduction........................... 66 4.2 Bivariate Spectral Analysis ................. . 66 4.2.1 Estimating the Spectral Density of Each Series .. . 67 4.2.2 Estimating the Absolute Coherency Spectrum. . . . 69 4.2.3 Estimating the Phase Spectrum. . . . . . . . . . . . 70 5 TRANS 72 5.1 Introduction........................... 72 5.2 Computing Cross Correlations. . . . . . . . . . . . . . . .. 72 5.3 An Overview of Transfer FUnction Modelling ........ 74 5.4 Fitting a Preliminary Transfer FUnction Model . . . . . .. 76 5.5 Calculating Residuals from a Transfer FUnction Model . .. 78 5.6 LS Estimation and Prediction with Transfer FUnction Models 80 6A~C ~ 6.1 Introduction........................... 86 6.1.1 Multivariate Autoregression. . . . . . . . . . . . .. 87 6.2 Model Selection with the AlCC Criterion .......... 89 6.3 Forecasting with the Fitted Model . . . . . . . . . . . . .. 89 7 BURG 91 7.1 Introduction ..... 91 Contents ix 8 ARAR 95 8.1 Introduction ............... . 95 8.1.1 Memory Shortening . . . . . . . 95 8.1.2 Fitting a Subset Autoregression. 97 8.2 Running the Program . . . . . . . . . . 98 9 LONGMEM 101 9.1 Introduction ..... . 101 9.2 Parameter Estimation 102 9.3 Prediction ...... . 104 9.4 Simulation ...... . 105 9.5 Plotting the Model and Sample ACVF . 106 Appendix A: The Screen Editor WORD6 108 A.1 Basic Editing . 108 A.2 Alternate Keys . . . . . . . 108 A.3 Printing a File ...... . 109 A.4 Merging Two or More Files 109 A.5 Margins and Left and Centre Justification 109 A.6 Tab Settings ... 110 A.7 Block Commands . 110 A.8 Searching ..... 111 A.9 Special Characters 111 A.lO Function Keys .. 112 A.11 Editing Information 112 Appendix B: Data Sets 113 Index 116 1 Introduction 1.1 The Programs The time series programs described in this manual are all included in the package ITSM (Interactive Time Series Modelling) designed to accompany the book Time Series: Theory and Methods by Peter Brockwell and Richard Davis, (Springer-Verlag, Second Edition, 1991). With this manual you will find two versions of the package, ITSM41 and ITSMSO (each on a 3!" diskette). The system requirements for ITSM41 are fewer than for ITSMSO (see Section 1.2), however ITSMSO can handle larger data sets (univariate series with up to 20000 observations and multivariate series with up to 10000 observations of each of 11 components). Both versions of the package contain the programs listed below. PEST is a program for the modelling, analysis and forecasting of uni variate time series. The name "PEST" is an abbreviation for Parameter ESTimation. SPEC is a program which performs non-parametric spectral estimation for both univariate and bivariate time series. SMOOTH permits the user to apply symmetric moving average, expo nential or low-pass smoothing operators to a given data set. TRANS allows the calculation and plotting of sample cross-correlations between two series of equal lengths, and the fitting of a transfer function model to represent the relation between them. ARVEC uses the Yule-Walker equations to fit vector autoregressive mod els to multivariate time series with up to 6 components (ITSM41) or 11 com ponents (lTSMSO) and allows automatic order-selection using the AICC criterion. BURG uses Burg's algorithm to fit autoregressive models to multivariate time series with up to 6 components (lTSM41) or 11 components (lTSMSO) and allows automatic order-selection using the AICC criterion. ARAR is based on the ARARMA forecasting technique of Newton and Parzen. For a univariate data set it first selects and applies (if necessary) a memory-shortening transformation to the data. It then fits a subset autore gressive model to the memory-shortened series and uses the fitted model to calculate forecasts. 2 1.2 System Requirements LONGMEM can be used to simulate data from a specified fractionally integrated ARMA model with zero mean. It can also be used to fit such a model to a data set (by maximizing the Whittle approximation to the Gaussian likelihood) and to forecast future values of the series. This manual is designed to be a practical guide to the use of the programs. For a more extensive discussion of time series modelling and the methods used in ITSM, see the book Time Series: Theory and Methods, referred to subsequently as BD. Information regarding the data sets included with the package is contained in Appendix B. Further details, and in some cases an analysis of the data, can be found in BD. 1.2 System Requirements ITSM41 : • mM PC (286 or later) or compatible computer operating under MS DOS; to run the programs in WINDOWS, version 3.1 or later is required; • at least 540 K of RAM available for applications (to determine your available RAM use the DOS command mem and observe Largest ex ecutable program size); if you have DOS Version 6.0 or later you can optimize your available RAM by running memmaker, • a hard disk with at least 1.1 Mb of space available; • an EGA or VGA card for graphics; • a mathematics co-processor (recommended but not essential). ITSM50: • mM PC (386 or later) or compatible computer operating under MS DOS; to run the programs in WINDOWS, version 3.1 or later is required; • at least 8 Mb of RAM; • a hard disk with at least 2.6 Mb of space available; • an EGA or VGA card for graphics; • a mathematics co-processor (recommended but not essential). When booting the computer, the program ANSI.SYS should be loaded. This is done by including the command DEVICE=ANS1.SYS in your CONFIG.SYS file.

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