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.