The change-point existence in climatological series being the main alternative to
randomness to be expected, its determination is the first operation to be proceeded in the
analysis.
Noting that for the trend statistic ti, we have the recurrence (Sneyers, 1958)
ti
= ni + ti-1,
(12)
a progressive trend analysis will
be given with computing ti, for i = 1, 2,.. , n, using (12). Standardised
values u(ti) of ti are then derived from the relation
u(ti)
= [ti - E(ti)]/s0(ti),
(13)
where s20(ti)
= var ti.
All the u(ti) values
having, with a good approximation, the standard normal distribution (var u = 1), absence
of internal trend will appear when all u(ti) values remain near zero.
On the contrary, if after the
value i = P, the values u(ti) diverge systematically from zero, P may be
considered as a first determination of a change-point. After the withdrawal of the
detected stable part of the series, the same operation may be used for further
determinations of other change-points.
An equivalent progressive
procedure may be made in computing the values u(t'i) for the series (xi,
xi+1,.. , xn), the progressive withdrawal being then operated on the
stable parts found at the end of the series. Moreover, P may be considered as dividing the
complete series into two stable partial series if u(ti) and u(t'i+1)
remain both near zero respectively for i = 1, 2,.. , P and for P+1, P+2,.., n.
Efficiency is, however, here
restricted by the fact that compensating trends may be hidden by non significant u(t)
values. Account has thus to be taken of alternating sequences of small or high ranks. In
this case, in a first determination, the points separating such sequences should be
accepted as possible change-points, even for sequences of only two elements.
