Process transformation¶
The objective here is to create a process as the image through
a field function
of another process
:
General case¶
In the general case,
is a multivariate stochastic process of dimension
where
,
a multivariate
stochastic process of dimension
where
and
and
is defined in (1).
We build the composite process thanks to function
and the process
.
The library proposes two kinds of field function: the value functions defined in (2) and the vertex-value functions defined in (3).
Trend modifications¶
Very often, we have to remove a trend from a process or to add it. If
we note the function
modelling a trend, then the field function which consists in
adding the trend to a process is the vertex-value function
defined by:
(1)¶
The library enables to directly convert the function
into the vertex-value function
thanks
to the TrendTransform object which maps
into the
vertex-value function
.
Then, the process is built with the object
CompositeProcess from the data:
and the process
such that:
Box Cox transformation¶
If the transformation of the process into
corresponds to the Box Cox transformation
which transforms
into a process
with stabilized variance, then the
corresponding field function is the value function
defined by:
(2)¶
The library enables to directly convert the function
into the value function
thanks
to the ValueFunction object.
Then, the process
is built with the object
CompositeProcess from the data:
and the process
such that: