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Unformatted text preview: Lecture Notes on Univariate Time Series Analysis and Box Jenkins Forecasting John Frain Economic Analysis, Research and Publications April 1992 (reprinted with revisions) Abstract These are the notes of lectures on univariate time series analysis and Box Jenkins forecasting given in April, 1992. The notes do not contain any practical forecasting examples as these are well covered in several of the textbooks listed in Appendix A. Their emphasis is on the intuition and the theory of the BoxJenkins methodology. These and the algebra involved are set out in greater detail here than in the more advanced textbooks. The notes, thus may serve as an introduction to these texts and make their contents more accessible. The notes were originally prepared with the scientific word processor Chiwriter which is no longer in general use. The reprinted version was prepared with the L A T E X version of Donald Knuth’s T E X mathematical typesetting system. Some version of T E X is now the obligatory standard for submission of articles to many mathematical and scientific journals. While MS WORD is currently acceptable to many economic journals T E X has been requested and is sometimes very much preferred. Many books are now prepared with T E X. T E X is also a standard method for preparing mathematical material for the internet. T E X is free and the only significant cost of using it is that of learning how to use it. It is often held that T E X systems are to difficult to use. On the other hand, it would have been impossible to produce this document in, for example, WORD 6.0a and WINDOWS 3.1x. I would not suggest that T E X be used for ordinary office work. A standard WYSIWYG word processor such as WORD would complete this work much better. For preparing material such as these notes T E X is better and should be considered. An implementation of T E X for Windows is available from me on diskettes. T E X and L A T E X are freeware. A distribution (gT E X) is available from me on request. I can also provide some printed installation instructions if anyone wishes to in stall it on their own computer. While gT E X is designed to work with Windows its installation and operation requires some knowledge of MS/DOS. I am not in a position to support any T E X installation. For a knowledge of L A T E X please see Lapont (1994), ”L A T E X document preparation system  User’s Guide and Reference Manual”, AddisonWesley Publishing Company, ISBN 0201529831. Contents 1 Introduction 3 2 Theory of Univariate Time Series 8 2.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Normal (Gaussian) White Noise . . . . . . . . . . . . . . . . . 10 2.1.2 White Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.3 AR (1) Process . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 Random Walk . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Lag Operators  Notation . . . . . . . . . . . . . . . . . . . . . . . . 12....
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 Spring '11
 stevenjulious
 Forecasting, White Noise, Autocorrelation, Stationary process, Time series analysis, Xt

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