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I have an annual time series of data of a growth-rate variable $X$ for 50 years. Most of the values for the variable $X$ are less than 10%. The exception are two values that are around 30%.

How do I treat these two values in the regression?

I would like to seek your suggestions in this regard.

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This would depend on what you know about the outliers. They should not be removed unless there is some obvious error. They could be indicative of interventions. First step is to understand why you have them. Then you can decide how to treat them. In addition to the covariate you might want to include autoregressive terms in the model. You may also want to investigate how the outliers affect the regression parameter for X (perhaps by using influence functions).

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  • $\begingroup$ Thanks Michael for the prompt response. The data are not due to error, but they are due to the intervention. I also included AR terms in the model.As to the influence functions, these two observation lie above the cutoff point suggested by Cooks distance. Is it okay to remove these observations in time series analysis? $\endgroup$
    – nic
    Jul 15 '12 at 14:12
  • $\begingroup$ @nic: If you know that they are due to an intervention, then add an indicator variable for the intervention. You'd have to decide what kind of impact the intervention would have: is it 1 in the year of the intervention and 0 otherwise, or is it 1 in the year of the intervention, 0.5 in the following year, and 0 otherwise, or ... The bottom line is that you have determined that the data is in fact legitimate and explainable, so add that explanation to your model. $\endgroup$
    – Wayne
    Aug 14 '12 at 14:04

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