I am looking at a new project involving time series analysis. I know I can
complete the tasks involving VARMA using either dse or mAr (and I think
there are a couple others that might serve).
However, there is one task that I am not sure of the best way to proceed.
A simple example illustrates what I am after. If you think of a simple
ballistic problem, with a vector describing current position in 3
dimensions, the components of that vector are simple functions of initial
position, initial velocity (constants, for our purposes) and time. It is
trivial calculus to compute these values at arbitrary time using only
initial conditions and time. Of course, for such a simple problem, we know
the equations of motion that we can use for this purpose.
I want to use time series values to estimate a suitable vector valued
function of time in a case where we know neither the equations of change nor
the initial conditions (but where we have daily values going back many
years). Actually, I don't really care much about the details of the
function nearly as much as the first and second derivatives of the function
with respect to time; and these derivatives have to be inferred from the
model of the measurements as 'simle' functions of time. And as I do not
want to assume the system is autonomous, I want to be able to repeat the
analysis on a moving window wherein always the current day is designated as
having s = 0 (I.E. the time variable used in the model estimated slides
along that representing real time). I figure that if that window is short
enough, a quadratic or cubic function of time will suffice. Finally, if the
combination of first and second derivatives indicates that the first
derivative will take a value of 0 at some point in the future, I want to
estimate the number of days until that happens. (yes, I know I will need
some sort of orthogonalization of the time variable in order to reduce
problems of multicollinearity, but that I'd expect in any multivariate
nonlinear regression).
I don't know if this could be recast as a VARMA problem, or if so, how and
how I'd get the answers to the questions of importance to me. I would
welcome being enlightened on this, if there is an answer.
The question is, "Is there a package that already provides support for this
'out of the box', as it were, and if so which one, or do I have to
construct
code supporting it de novo?"
Thanks
Ted
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