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By Petr Mandl

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8) to structural parameterization in vector autoregressive models was considered in Ahn (1988). 1 Causality The problem of causal relationship has been a fascinating subject for both philosophers and statisticians for centuries. In statistics, when a student first comes across simple correlation analysis, he is usually cautioned that a significant cross-correlation does not necessarily imply a cause and effect type relationship. On the other hand, it is difficult to define clearly what causality means.

We have the innovation outliers (IO) if the noise process at has a heavy tailed distribution compared with the normal distribution. This type of outlier is less problematic if at has finite fourth order moment. 5). Another more serious type of outliers is known as the additive outliers (AO). 1), and Wt is a contaminating process with P (Wt = 0) = C for some C with 0 ≤ C ≤ 1. The presence of Wt masks the original autocorrelation structure of Xt and hence causes greater problems in the modeling of Xt .

1 that the observations at t = 83 and 84 are somewhat larger than the rest of the series and may be regarded as outliers. 2 the series can be identified as an AR(1) process because the partial autocorrelation has a cut-off after lag 1. The two observations were then replaced by observations from the same months in the previous year (1971). 4 gives © 2004 by Chapman & Hall/CRC the sample autocorrelations and the partial autocorrelation. It can be seen that the dependence structure of the series is now much stronger and the partial autcorrelations suggested an AR(2) model instead.

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