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# ch05 - Chapter 5 Forecasting Li Chen Department of...

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Chapter 5: Forecasting Li Chen Department of Mathematics University of Bristol 1 / 7

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Introduction Forecasting future values of an observed time series is an important, but difficult task. Suppose we have an observed time series x 1 , . . . , x N . We would like to be able to forecast or predict the values of x N +1 or more generally x N + r for r ∈ N Notation ˆ x ( N , r ), the prediction of x N + r made at time N . The natural number r is called the lead time (or step ahead ). There is no single best procedure. Different procedures will be more successful than others depending on the applied situation. 2 / 7
Introduction (Contd) The main difficulties are: (a) assuming that the historical conditions that generated the series will remain the same in future; (b) even assuming (a) it is possible to fit many valid models to the data and for all of these to give very different predictions; (c) assuming (a) and (b) are no problem and we have fitted the “correct” model then the parameters are still only estimates and therefore probably not exactly the true parameters. Therefore

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