How to apply a AR(MA) model to a prewhitened signal?

Question

I have two (vehicle velocity) signals that should consist of similar "latent" drivers, but have different autocorrelation structures. The driver-signals are quite nasty statistically, so I'm not attempting to model them.

I can get quite nice results by prewhitening the signals using AR(1)-residuals, but these are very difficult to interpret in "real world terms" (ie. velocities). So what I'd like to do is to prewhiten one of the signals and then add the AR-model of the other signal to this, so that I'd have two signals with same autocorrelation structures.

It may be that there is a very simple method for doing this, but unfortunately I haven't found one. I guess it should be sort of an inverse of the Yule-Walker method. One also that is quite close is to use arima.sim with innovations, but with the difference that I don't have innovations, but residuals.

Answer 1

I am not quite sure what you are trying to do and I'm not sure what you mean by "add the AR-model". However, here is some direction:

1. You could fit an ARMA model to one dataset and then write your own down to use those coefficients on another dataset.
2. Take a look at the forecast package and the function Arima() and auto.arima() . There is also R's arima() .