New PDF release: A course in time series analysis

By Daniel Peña; George C Tiao; Ruey S Tsay

ISBN-10: 047136164X

ISBN-13: 9780471361640

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Example text

This has the undesirable property of placing comparable weight, although of opposite sign, on the earliest and latest points of the data. For prediction it is desirable that much greater weight be placed on later data, closer in time to the values that are being predicted. 1b on a much enlarged scale compared with the series. The persistence shown in these errors, specifically, the tendency for one value to be close to the previous value, could be used to improve the prediction. Various methods have been used to overcome these criticisms, notably the use of regression with heavier weight placed on the most recent values; the weights typically are discounted into the past.

1988). The Statistical Theory of Linear Systems. Wiley, New York. Hardle W. (1990). Applied Nonparametric Regression. Cambridge Univ. Press, Cambridge, UK. Hardle, W. et al. (1998). Wavelets, Approximation and Statitical Applications. Cambridge Univ. Press, Cambridge, UK. Harvey, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge Univ. Press, Cambridge, UK. Hendry, D. F. and Clements, M. P. (1998). Forecasting Economic Time Series. Cambridge Univ. Press, Cambridge, UK.

1. 3 illustrate a variety of time series. Let us start by looking at these from the point of view of linear prediction. By prediction we mean estimation of one or more values of the series using previous values. A linear prediction is one that can be represented as a linear combination of the previous values. The simplest linear prediction method is to extrapolate a deterministic curve fitted to the time series by linear regression. This curve may, for example, consist of polynomials for trend, sinusoids for cycles, and indicator variables for seasonality.

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A course in time series analysis by Daniel Peña; George C Tiao; Ruey S Tsay


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