# [R] TS model

From: Ted Byers <r.ted.byers_at_gmail.com>
Date: Tue, 08 Jun 2010 11:35:06 -0400

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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