The seasons or seasonal cycles to be tested can be chosen through
an indicator variable defined in the argument sid
.
By default, all the \(t\)-statistics
related to each individual dummy or cycle and the joint \(F\)-statistic
are returned.
If type = "dummy"
, the index of the target seasons can be specified in sid
.
For example, in a quarterly series:
sid=c(2)
returns the test statistic to the stability of the second quarter;
sid=c(1,3)
returns the joint test statistic for the first and third quarters;
sid=c(1,2,3,4)
returns the joint test statistic for the null of seasonal
stability at all seasons.
If type = "trigonometric"
, the indicator vector sid
must be of length
floor(frequency(x)/2)
and will consist of ones and zeros. Each element in
sid
is related to each seasonal cycle according to the same order in which
the seasonal frequencies, \(w_j\), are defined: \(w_j=2\pi j/S\), \(j=1,...,Sh\),
where \(S\) is the periodicity and \(Sh\) is floor(frequency(x)/2)
.
For example, in a monthly series:
sid=c(0,0,0,0,0,1)
returns the test statistic to the stability of the cycle with
frequency \(w_6=\pi\);
sid=c(1,0,0,0,0,1)
returns the joint test statistic for cycles related
to frequencies \(w_1=\pi/6\) and \(w_6=\pi\);
sid=c(1,1,1,1,1,1)
returns the joint test statistic for the stability of
all seasonal cycles.
The following keywords are also admitted:
sid="all"
, computes all the test statistic related to each individual season
or cycle as well as the joint test statistic for all seasons or cycles;
sid="joint"
computes the joint test statistic for all seasons or cycles.