My question is a bit general

Say I am given a time series $X_t$, In what ways I can use in order to check whether the sequence behaves like a stochastic trend model or not? and if yes how can I find the best fit model?

(i.e. $X_t=X_{t-1}+c+U_{t-1}$ where $U_{t}$ is some zero mean and stationary process)?

  • $\begingroup$ look for posts on "unit root test" or "Dickey-Fuller" on this site $\endgroup$ – Christoph Hanck May 30 '15 at 15:56

Identify an ARIMA model. If first differences are needed then include a constant/trend in the model. If the constant is significant then you can conclude that a stochastic trend is appropriate. Other kinds of "trend models" such as a deterministic trend variable of the form X=1,2,,,,,t might be more appropriate. Testing alternatives is always a good idea.

  • $\begingroup$ Thanks, can you recommend me a specific test? $\endgroup$ – roshe May 30 '15 at 15:41
  • $\begingroup$ the test statistic is the t value associated with the constant. You can obtain it in this case by simply lagging the y series 1 period and estimating a lagged regression using the lag as a predictor. $\endgroup$ – IrishStat May 30 '15 at 16:01

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