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I came across this question online that's from a math/stat challenge a while back. Would love to get some thoughts on what the correct answer should be:

You're trying to assess transit usage trends in a region that exhibits significant tourist traffic. It seems that your data may be heteroskedastic, as none of your predictors are producing good standard errors. Which of the following techniques would be LEAST logical as an immediate next step in mitigating this problem?

  • A. Removing seasonality from the transit data
  • B. Differencing between time steps in your time series data
  • C. Adding data that is lagged by 12 months as an additional covariate
  • D. Adding data about the number of airline flights into and out of region as an instrumental variable
  • E. Logarithmically transforming your independent variables

My thoughts:

  • A. Seems reasonable. While I'm not sure seasonality will always cause conditional heteroskedasticity in the regression model, we should always remove non-stationary components like seasonality from a time series before fitting regression.
  • B. I feel differencing here is more about alleviating potential "trend" component and would not help with heteroskedasticity
  • C. I'm not sure here. I feel like adding a lagged dependent could address autocorrelation caused by model misspecification. But don't see how it helps with heteroskedasticity or seasonality.
  • D. While adding a missing variable could help with heteroskedasticity, isn't number of airline flights itself a seasonal/non-stationary variable, which could cause problems?
  • E. I feel like this won't help that much if we don't do the same for the dependent variable?

Would really appreciate any input!

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