In my limited experience of running economic models, I've come to find what seems to me like a paradox.
Most models in the literature of, say, the inflation rate are run in levels. This is notwithstanding the fact that the data is generally speaking I(1), but without cointegration in order to justify it. In a standard OLS model, I know this results in spurious correlation and thus biased estimates, in which case forecasts from such models are useless. The same, I believe, is true for VAR/VARMA/ARIMA-style models. The problem, however, is that economic theory seems to dictate running the models in levels. I've spoken to some professors about this, and they argued that some researchers will run a model in levels and apply HAC standard errors to raise the bar somewhat for statistical significance, even if the data is nonstationary. I know this is a reasonable correction for serial correlation, non-normality, or heteroskedasticity, but I know of no real corrections for lack of stationary other than differencing or otherwise transforming the data.
Other options I've seen include alternate methods of estimation, including perhaps fitting, say, an ARMA process to the residual series or estimating the model with a Kalman filter. I'm interested in learning -- and I apologize for my lack of knowledge on this subject -- how I could go about fitting these models to nonstationary data, without accepting spurious correlation or using what appears to be an "easy way out" through simply applying -- and probably misapplying -- HAC standard errors.
I would greatly appreciate any insights anyone could offer. I'm very much interested in learning new models, so please feel free to suggest a model even if a recent undergraduate like myself would normally not have much experience with them. (I've seen, for example, but am not too acquainted with error-correction models; I don't think these correct stationary, but it's something I'll surely look into further.)
Thanks in advance.
