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By A. C. Bajpai, Irene M. Calus, J. A. Fairley (auth.), C. N. Hewitt (eds.)

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Another approach is based on taking the Pth percentile of n ordered observations to be the (P/lOO)(n + l)th value. C. BAJPAI, ffiENE M. A. e. 260 and 488. For a larger set of data, the choice of approach would have less effect. 3 The mean absolute deviation Although the interquartile range may be an improvement on the range, it still does not use to the full all the information given by the data. Greater use of the values recorded would be made by a measure which takes into account how much each value deviates from the arithmetic mean.

If r(n) is insignificantly different from zero for any other lag, then there is no significant relationship at lag 11; if r(n) is close to unity, then there is a significant positive autocorrelation at lag n; and if r(n) is close to minus unity, then there is a significant negative autocorrelation at lag n. Thus for a strongly seasonal series of period p samples, we would expect the lagp autocorrelation to be highly significant and positive; and the lagp/2 autocorrelation to be highly significant and negative.

2 and 5). Here identification is normally accomplished by reference to a statistical structure (or order) identification procedure, of which the best known is that proposed by Akaike;6 while estimation of the parameters characterising this identified model structure is normally accomplished by least squares or recursive least squares procedures, as discussed in Section 3. The partial autocorrelation function (PAF) exploits the fact that, whereas it can be shown that the autocorrelation function for an AR(n) process is theoretically infinite in extent, it can clearly be represented in terms of a finite number of coefficients, namely the n parameters of the AR model.

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