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In a time series regression model I am working on, our intervention happened just several months after an big influential external event. The full time series model, therefore, underestimates the external event, but puts more weights on our intervention effect. However, we know that this is not quite correct from other researchs and domain experts. So the current remedy is to give an estimated effect to the external event associated with a given distribution, say the Normal distribution. After simulating for $N$ times, we plug this simulated number as a fixed value in the model, the rest of the coefficients are still estimated from the R software (using "arima" function). Therefore they result in $N$ models, or less.

Based on this approach, the distribution of some coefficients are not normally distributed. My question is:

  1. Should I still choose the model based on the model selection criteria, or should I summarize each coefficient as a distribution?

  2. There is a parameter originally not statistically significant, but with the expected sign. I kept it there as a confounding because it could change the estimate of the intervention parameter by 10%. If we summarize coefficients as distributions, the standard deviation of this distribution is much smaller than the standard error of the coefficient in the full model. And the 95% confidence range does not contain zero as well. Therefore how should I treat it for the reporting purpose, which goes back to Question 1, how should I summarize the models due to this method?

It will be really appreciated if someone can provide some suggestion.

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Have you tried to include another regressor (like a dummy variable) in your model to capture the effect of your big external event and improve the fitting over that? – Stat Aug 17 '12 at 19:20
The external event was modelled as "level change" (0,0,0,1,1,1) and "trend change" (0,0,0,1,2,3). But the coefficient in the full model is too small to be true (even thought it is statistically significant). That's why we adopt the alternative approach to give it a fixed number in the model. – Fred Aug 18 '12 at 1:58

1 Answer

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You say "The full time series model, therefore, underestimates the external event, but puts more weights on our intervention effect." . I say you must have the wrong model. Please post your data and your assumption about the time and type of intervention and I will try and provide you with a more appropriate model. The approach would be to implement the work of http://www.unc.edu/~jbhill/tsay.pdf and to incorporate robustly identified ARIMA structure.

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It's a medical data on one particular drug usage. The judgment of how big the impact of this event was based on the clinical reason and other researches on the reaction of this event around the global, which turned over the series to decrease. The event happend 7 months before our intervention started. The intervention was measured as cumulative number of participation. The full models considered were Box-Jenkin's techinque and deterministic trend and seasonal regression with ARMA errors. But with both approaches, the coef of the event is not big enough to turn over the series to decrease. – Fred Aug 19 '12 at 3:42
In both models the decreasing segment in the series was largly contributed by our intervention. That's why we adopt the alternative to fixed the coef of the event. – Fred Aug 19 '12 at 3:49
And the data is where ? – IrishStat Aug 19 '12 at 23:12

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