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In an assignment of time series analysis, I am asked to compare an intercept-only model with a slope model. I understand that the intercept-only model is just a regression model that only includes the constant term. But how about the slope model? I appreciate it if anyone could explain what a slope model refers to.

Jack Learning stats
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  • Related: https://stats.stackexchange.com/questions/504931/how-to-interpret-the-random-effect-of-a-random-slope-model – Galen Nov 29 '23 at 15:49
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    It may well be simply a regression on a linear trend of time. You can model this by using a single regressor containing the time difference (in days, months, or years, whatever your time granularity is) to some fixed anchor date. Alternatively, it may be an I(1) model. Best to ask your instructor or teaching assistant. – Stephan Kolassa Nov 29 '23 at 15:52
  • @StephanKolassa Thank you very much. If I used ARIMA(0,1,1) with 50 time points and included intervention terms in the model, would this model become a slope model? – Jack Learning stats Nov 29 '23 at 16:00
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    Hm. There is no "commonly accepted" definition of a "slope model" in time series analysis, which is why I would recommend you talk to your instructor. An ARIMA(0,1,1) is an MA model on first differences, so it has something to do with slopes... but I don't think I would call it a "slope model". In R, run this a few times: plot(arima.sim(model=list(order=c(0,1,1),ma=0.7),n=50)), perhaps changing the ma parameter to something negative... yes, there are slopes in the plot, but they are local ones. – Stephan Kolassa Nov 29 '23 at 16:56
  • @StephanKolassa Thanks much again! This explanation is very helpful. I learned that ARIMA can help remove overall trends and make the series stationary. But what confused me the most was that I was asked to use a "slope" model when I used ARIMA to estimate the intervention effect by including an intervention term (not doing forecasting). Would this be conventional? – Jack Learning stats Nov 29 '23 at 20:02
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    Running a regression on an intervention variable with ARIMA errors is a possibility (though if you just look at the significance of the intervention parameter, the ARIMA part is really doing nothing. ARIMAX is hard to interpret. See here for the difference. I am a bit at a loss what either one has to do with a "slope model"... best to go back to who gave you that advice and ask for clarification. – Stephan Kolassa Nov 30 '23 at 06:19

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