TIPS seasonal adjustments: the outlier factor

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Kevin M
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TIPS seasonal adjustments: the outlier factor

Post by Kevin M »

There has been an awareness of the impact on seasonality on TIPS yields in this forum since at least 2014--see Seasonal Indexation Impacts in TIPS Prices and Yields, for example. In a 2020 thread I summarized the forum's latest understanding of seasonal adjustments and how to calculate them: TIPS yield curve and seasonal adjustment update.

Something I've been seeing for more than a year now is that even after seasonally adjusting TIPS yields, there remain some fairly consistent irregularities in the yield curve. Here's a chart of ask and seasonally adjusted ask yields through Jan 2034 using TIPS ask quotes from Schwab on Friday (yesterday), Jul 5, 2024:

Image

(I've truncated the vertical axis to emphasize the curve irregularities.)

Note the seasonally adjusted (SA) curve (red) is quite smooth from Jan 2029 through Jan 2034, but there are spikes in the SA curve before that; the reason is because the spikes are for Oct maturities, and there are no Oct maturities after 2028. The most notable spikes are for Oct 2027 and 2028.

So what's causing the Oct spikes?

I've looked at coupons and index ratios as possible causes, but based on the relationships between these for Oct and nearby maturities, it doesn't look to me like either of these explain the spikes.

The Oct 2027 and 2028 maturities do have relatively low index ratios, at 1.05886 and 1.02407 respectively, but the Apr 2028 1.250% TIPS also has a relatively low IR of 1.04573, and the April 2029 2.125% also has a low IR of 1.01409, yet we don't see spikes in the SA curve for these. Also, one would think that if anything the lower IRs would increase demand, which would increase price and lower yield, but we see the opposite in the SA curve.

The Oct 2027 coupon is 1.625%, but the Jul 2027 coupon is lower at 0.375% and the Jan 2028 coupon is higher at 1.750%, so coupon doesn't seem to explain it.

As mentioned in the seasonal adjustment update thread linked at the beginning of this post, I method I use to do the seasonal adjustments is from the paper Seasonally adjusted prices for inflation-linked bonds, written by Paul Canty. In that paper Canty reviews a method for extending the seasonal adjustment to include what he refers to as an outlier index, about which he says:
The term Ot is called the outlier index and contains information about expected future one-off shocks to the inflation
index.
Having no other explanation, and not understanding what "one-off shocks" might explain the October anomaly, I just incorporate an empirical factor that does some additional smoothing of the curve, so I end up with this:

Image

I'm posting this primarily to see if I can get some forum brainpower applied to why we might see these residual yield curve irregularities after applying the seasonal adjustments. Note that the Oct 15 maturity ref CPIs are based on interpolation between the Jul and Aug CPI values, so it seems to be related to some expectations about the CPI in mid-summer going forward that's not reflected in the seasonality factors for summer of 2023, which are the latest we have available to do the seasonal adjustments for 2024.
If I make a calculation error, #Cruncher probably will let me know.
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B88
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Re: TIPS seasonal adjustments: the outlier factor

Post by B88 »

I have nothing to add other than I have noticed this as well. I hope someone knows the missing factor.
Walkure
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Re: TIPS seasonal adjustments: the outlier factor

Post by Walkure »

On another thread discussing the variance between breakeven and realized inflation, I posed the question (which user FactualFran answered with a very interesting chart) whether the Core CPI breakevens more closely tracked realized than the overall CPI breakevens did. If indeed that feature bears out, it suggests that the marginal TIPS trader is using them as a kludgy back door way of hedging Core inflation. As such, if there were a structural reason why the mid-summer core seasonal adjustment factor was more (less?) pronounced than that of overall CPI, then that might explain some of the under-adjustment.
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Kevin M
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Re: TIPS seasonal adjustments: the outlier factor

Post by Kevin M »

Walkure wrote: Sat Jul 06, 2024 8:53 pm On another thread discussing the variance between breakeven and realized inflation, I posed the question (which user FactualFran answered with a very interesting chart) whether the Core CPI breakevens more closely tracked realized than the overall CPI breakevens did. If indeed that feature bears out, it suggests that the marginal TIPS trader is using them as a kludgy back door way of hedging Core inflation. As such, if there were a structural reason why the mid-summer core seasonal adjustment factor was more (less?) pronounced than that of overall CPI, then that might explain some of the under-adjustment.
Interesting.

Here's a plot of core CPI minus CPI, both seasonally adjusted, for the last five years:

Image

The peak of this plot in 2023 was in June; I'm not sure exactly what to make of this aside from the fact that the time period fits. Note that in 2022 the opposite occurred, with the negative peak in June.
If I make a calculation error, #Cruncher probably will let me know.
Walkure
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Re: TIPS seasonal adjustments: the outlier factor

Post by Walkure »

Kevin M wrote: Sun Jul 07, 2024 9:57 am
Walkure wrote: Sat Jul 06, 2024 8:53 pm On another thread discussing the variance between breakeven and realized inflation, I posed the question (which user FactualFran answered with a very interesting chart) whether the Core CPI breakevens more closely tracked realized than the overall CPI breakevens did. If indeed that feature bears out, it suggests that the marginal TIPS trader is using them as a kludgy back door way of hedging Core inflation. As such, if there were a structural reason why the mid-summer core seasonal adjustment factor was more (less?) pronounced than that of overall CPI, then that might explain some of the under-adjustment.
Interesting.

Here's a plot of core CPI minus CPI, both seasonally adjusted, for the last five years:

Image

The peak of this plot in 2023 was in June; I'm not sure exactly what to make of this aside from the fact that the time period fits. Note that in 2022 the opposite occurred, with the negative peak in June.
The chart you have does not quite capture what I'm describing. Subtracting SA CPI from SA Core CPI does not give the exact difference because the two datasets receive different seasonal adjustments.
Here is a plot of just the seasonal adjustments for all-items CPI. Over the course of a 12-month rolling period they vary from (-.8 to +1.1) but approximately cancel out to zero, of course.
Image

Now here is a plot of just the seasonal adjustments for Core CPI. There is a slight difference in the shape of the sawtooth, but more importantly note the difference in the magnitude of the seasonal variance (-.6 to +.6):
Image

Finally, subtracting the Core seasonal adjustment factor from the overall seasonal adjustment factor gives the disparity in seasonality, which exhibits a somewhat predictable pattern of its own, which is to say that all-items CPI has the same seasonality, just to a greater degree than Core:
Image

Note also that June is one of two points in the year where the seasonal adjustment in both series is essentially 0. I'm not entirely sure what the significance of that is but I suspect that there's an interplay between the non-seasonal principal adjustments and the degree to which All-Items CPI deviates from Core CPI over the course of a year. In other words, All-Items does a better job of approximating/hedging Core when the seasonal adjustment is around zero and a worse job when the seasonal adjustment has high absolute value.
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