In this case study on treasury yeilds from MIT, I have a question on page 11-12. He uses this data

getYahooData("^TNX", start=20000101, end=20130531)

His logic on page 11 is this

  • "only daily is close to being stationary" (I get this)
  • "we observe lower p value when higher freq frequency" (I see this since p-value daily < p-value monthly)
  • "so stronger time series structure at higher freq, hence we diffrence the data"

for that data, we reject H0: non-stationary.

I want to understand how he can go from seeing the p-values are lower for daily (closer to stationary) into knowing that differenced data will reject H0.

  • 1
    $\begingroup$ @dysonance gave a good answer, but I'll just emphasize that my question was rather "why is this step done in the analysis" and the answer is: standard procedure, and it's done in order to meet the assumption of the model. $\endgroup$ – jacob Mar 2 '16 at 21:27

As far as I know, it's impossible to know that the differenced data will stationary (reject H0). That being said, when we have a time series that is non-stationary, the first thing a lot of econometricians do is difference the data. Still stationary? Difference it again!

After skimming the reference you gave, I don't think he's making the assumption that the first-differenced series will be stationary. My guess is that he knows that to be the case beforehand and is simply demonstrating it. Unless I'm missing something, it's not possible to know a non-stationary time series will become stationary after differencing it once without performing the unit root test on the differenced data.

(FYR: How many times you have to difference something until it's stationary gives you the order to which the series is said to be integrated.)

At the risk of editorializing, I once had a statistics professor whose biggest complaint about time series & econometrics was an apparent obsession with differencing data just to make the math work.

  • $\begingroup$ Ok, so it's a standard procedure ("Still stationary? Difference it again!") and we do it because rejecting H0 is needed to make the assumption of stationarity to hold. $\endgroup$ – jacob Mar 2 '16 at 21:26
  • $\begingroup$ Yes, you got it :) $\endgroup$ – Jacob Amos Mar 2 '16 at 21:27

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