So I've been looking at autocorrelation in the time series of UK CPI inflation this morning (because that's just what geeks do on Sunday mornings), and I noticed that there is little month-by-month autocorrelation, but a strong correlation with a 6-month lag and an even stronger one with a 12-month lag.
I guess the 12 month result is because some months tend to be similar each year (eg low inflation in January because of sales), but why the 6 month result?
It depends on whether you were using seasonally adjusted or unadjusted data. If you are calculating the annual (year-on-year) inflation rate using unadjusted data, then it *should* remove the 12-month autocorrelation. But because seasonal adjustment factors are estimated using moving averages fitted to the raw seasonal factors, there will be some 12-month autocorrelation.
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With year-on-year inflation calculations, you should get month-on-month autocorrelation, but it's spurious, because each month's annual rate of change has 10 months' data in common with the previous month's year-on-year change.
If the data are month-on-month, the autocorrelation *should* be low, because the error terms are so large,
@Nigel_Purchase I'm using month-by-month inflation. And indeed the autocorrelation is low for most lags, except for the 6 and 12 month lags.
I'm using the data from here.
I don't think it's seasonally adjusted, though maybe I should look into that a bit more just to be sure.
https://www.ons.gov.uk/economy/inflationandpriceindices/datasets/consumerpriceindices
Adam Jacobs 🇺🇦
Fight the Right