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I am running an interrupted time series analysis. (Basically, I run a "before" and "after" linear regression, and measure the change in Constant/y-intercept.)

My objective: to measure the sudden drop in prescribing rate of a certain drug, which occurred at time t. I want to prove that case A is singificant, and cases B and C saw no change.

Everything I've read seems to indicate:

  1. You adjust for seasonality, but you don't transform to remove trend from the data. (Because trend is usually relevant to your study.)
  2. ARIMA(1,0,0), that is, a single order of autoregression, seems pretty standard.

My question: when are higher levels of autoregression appropriate in ITS design?

I'm using weekly data, so there's a fair amount of noise. My data looks like this: Number of prescriptions per week

and my Ljung-Box test tells me that there's still autocorrelation in my data. enter image description here (Significance <.05 means there's likely more autocorrelation in the data)

Should I use a higher order of autoregression? Importantly, will doing so inappropriately underestimate the sudden change at time t?

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  • $\begingroup$ Your terminology could use a revision. Autocorrelation at lag greater than one is not the same as autocorrelation greater than 1. Also, in ARIMA models you have autoregressive order (not autocorrelation order). $\endgroup$ Commented Sep 23, 2016 at 16:36
  • $\begingroup$ Thank you for correcting my terminology, you're right. Does anyone have any thoughts on my problem, even if you don't have a complete answer? $\endgroup$ Commented Sep 30, 2016 at 14:55

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