Comments
gatogetaway OP t1_j0chvzz wrote
>A general audience would probably find this confusing without additional explanation.
Agreed. Fortunately, the audience here tends to be more chart savvy.
The YOY CPI change for November (centered on 11/15) is reported around 12/15, so that introduces 1 month of delay right off the bat.
A YOY change is also an average of the 12 most recent monthly inflation numbers (actually averaging log(1+MonthlyInflation) and annualizing it is more accurate). Regardless, an N-sample average introduces a signal delay of (N-1)/2.
In the case of YOY, the delay is 11/2, or 5.5. Add on the 1 month of delay in the reporting and you have 6.5 months. So, the number reported on 12/15 actually represents the inflation on 6/1.
tyen0 t1_j0ee6gl wrote
I don't see how a moving average is half of the timeframe out of date. It's certainly influenced by the most recent month, too.
gatogetaway OP t1_j0ewdep wrote
It is delayed by the (N-1)/2 timeframe. But you're right that it's certainly influenced by the most recent month too.
One way to think of it is it's influenced by all 12 months, and the average age of the data for those 12 months is about 6 months old.
The derivation can be found in Understanding Digital Signal Processing by Richard Lyons. In signal processing, filters similar to moving averages are commonly used, and the delay of that signal can be absolutely critical to the functional design of the system.
tyen0 t1_j0f0f7h wrote
I see what you are saying, I guess it's more of a semantics issue, and just eyeballing the data I think people can get how the moving average is lagging, but "exactly 6.5 months out of date" just seems a bit too harsh of a way of phrasing it.
That aside, I think this is a pretty cool visualization.
gatogetaway OP t1_j0f1ybr wrote
Thank you. Cheers!
EconomistPunter t1_j0cf90i wrote
Month-over-month numbers get revisions.
Not eliminating seasonality also means that your month-over-month numbers have an additional bias.
gatogetaway OP t1_j0cg2ca wrote
Fair points. I used not-seasonally-adjusted numbers because the YOY effectively eliminates seasonal effects.
rmm30 t1_j0cdrd9 wrote
Can you please add some explanation? For example, if the Nov CPI was +0.1%, why do you show that as < zero? I would have thought it’s approximately 1.2% annualized?
gatogetaway OP t1_j0cii18 wrote
You are right if seasonally adjusted numbers are used.
However, the values are not seasonally adjusted because seasonal adjustments don't really apply (or shouldn't) to YOY numbers, the focus of the chart.
The main idea is the YOY numbers are well out of date by the time they're published and may not reliable indicators of the current state of prices.
DeathMetal007 t1_j0ds7k4 wrote
I know economists rarely use error bars, but how much of the graph would be covered by error bars if you had to add them?
gatogetaway OP t1_j0ewlus wrote
Great question and I don't have an answer. However, given the volatility of the monthly measurements, the error bars could be quite large.
gatogetaway OP t1_j0cawfo wrote
Source: BLS.gov
Tool: Excel
Note that 4 out of the last 5 months, inflation has roughly been at or below the target inflation.
New-Post-7586 t1_j0f6wuv wrote
This data is great! Can you mock this up monthly and post please?
gatogetaway OP t1_j0f737w wrote
Sure, why not? I keep the spreadsheet up to date anyway.
Thank you!
[deleted] t1_j0f4j7b wrote
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[deleted] t1_j0frurf wrote
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cheapdad t1_j0cc2lw wrote
That's an insightful chart, but I say this as an economist who understands the difference between year-over-year and month-over-month rates of change, the concept of annualization, etc. A general audience would probably find this confusing without additional explanation.
When you say the year-over-year CPI change is "exactly 6.5 months out of date", are you saying that (for example) the December 2021 to December 2022 is really capturing the rate of change at the midpoint of that time period (mid-June)? Other than the reporting lags, I'm not sure what you're including in the concept of "out of date".