Many time series methods are oriented solely in terms of forecasting (e.g., ARIMA). However, it seems like a growth curve modeling framework (i.e., random coefficient modeling) can do virtually everything else. For instance instead of performing interrupted time series analysis via segmented regression, one can just use a discontinuous growth model. To account for autocorrelation, AR terms can be included within the level-1 growth curve model as well. Even seasonal models (i.e., harmonic and those with indicator variables) can just as easily be used within the growth curve modeling approach at level-1. It also handles multiple “subjects” much better; rather than having to perform a multivariate time series analysis, the growth curve model naturally accommodates additional sources of observations (e.g., people, economic indices).
So my question is:
Am I missing something, or is time series analysis (for all intents and purposes) just a collection of forecasting methods, with any explanatory modelling handleable by the regular multilevel growth curve model?
It seems to me that this might be the case, as there is no essential difference between time series data and longitudinal in data, other than time series are longer and generally pertain to an in-depth analysis of one “subject” (e.g., GDP; see Difference between longitudinal design and time series).