I have collected data at regularly spaced time intervals, and at each time, the observed data is commonly fit by a simple parametric functional form involving several parameters.
A naive approach to forecasting would be to treat each parameter as a univariate time series and use some forecasting method, like ARIMA, to forecast each of the parameters at some future time. Together, the forecast parameters would create the functional forecast at that time. I assume that potential correlations between the time series would make this problematic. Is that true? Is there a way to determine if it's actually not that big of a problem?
Otherwise, I guess you could use a multivariate time series forecasting approach, like VAR, although I am less familiar with those. Would such an approach be reasonable? What are some issues that would arise with forecasting in this way?
Is there a reference about this particular approach to forecasting and how it may be implemented?
