GISTEMP long range from yesterday is already out of date and is ~0.15 C warmer than the split offset between the 3 ensembles.

GEFS medium-range still being the highest of the three in the middle of the month. (long-range is even with prophet extended GEFS)

If I was going by intution on these dynamic models alone, I'd say there was still more room for correction, and I'd put more probability mass in the 1.145-1.195 bucket than the 1.22 C suggested by the medium range models alone. (An offset of -0.15C versus -0.10)

However, the pure statistical model is still pointing towards the upper most bucket as deserving of most of the probability mass (latest 1.26C). Today I ran a pure simulation using GARCH on the residuals from the ERA5->GISTEMP linear regression so I could jointly simulate a distribution about the mean temp (from the std dev derived from the statistical ARIMAX model) and accounting for the volatility of these residuals. Rather than a simple count for efficiency I relied on just sampling different ranges of CI (alpha=0.005 to 0.995 in order to cover both sides of the upper and lower CI); the result is a pseudo density-looking map (red upper CIs, blue lower CIs), where far from the green (expected) probability I interpret as probabilities less plausible given by this simulation (nearly white or nearly black areas as implausible):

GEFS long-range run finished ~ hour ago. Slightly cooler than last week's temps for the same period, but still showing seemingly implausible temps (low confidence this far out).

The end of the medium range models (~15 days) continue to show high temps tracking near 2024 for the start of May (if not a bit cooler at the end of the first week). 2024 anomaly was 1.32 C.

For the current GEFS long range, the implied 1.4 C anomaly for April seems implausible given a slightly cooler start to April though.

GEFS long range from Wed. (ARIMA adjusted to ERA5) still shows some seemingly implausible temps. The end of the medium range GEFS (tau=384h) is also quite a bit above the recent GEPS means and recent ECM runs.

Only two of the (non-arimax) members for May 31 are below 2024's temp (16.52) for the same day. The arimax-adjusted mean is ~ 0.1C higher at 16.63 C for May 31, 2025 compared to the previous year.

This is suggesting an anomaly of ~ 1.35 C for May which still looks on the high end given GEPS, ECM trending a bit lower for the middle of the month. (The mid range split offset between the three models + Prophet for the latter half alone suggests 1.28 C)

@parhizj Interesting. Polymarket's next to least favourite at 22% is >1.24
most favoured 1.05-1.09 32% and 1.1-1.14 32%
https://polymarket.com/event/may-2025-temperature-increase-c

@ChristopherRandles I didn't comment for lack of time, but I've reworked and validated a new purely statistical model over the last few days using only ERA5 data (ARIMAX with a single pair of day of year harmonics as exogenous seems the best model); this suggests an anomaly for ~ 1.26 C for May (15.93 C ERA5 temp) (the variance is almost entirely dominated by the ERA5->GISTEMP uncertaintly).

This temp is roughly coincident with the medium range estimate from the models that is extended by Prophet; the long-range GEFS though estimate is even higher as GEFS though is on the highest end.

Polymarket seems increasingly in favour of 1.1-1.14 now 35% and over 1.24 down to just 7%. Seems like good odds available if you believe your 1.26 C.

@ChristopherRandles check #memes

Polymarket odds are adding up to way above 100 Pct

@parhizj That is true, total 122% when I just looked. How you spread that between the options is likely to reduce the difference. There is also a range between buy and sell. So for example you can only buy over 1.24 at 10% despite the 7% headline figure shown.

Still a good value option if you think it likely?

@ChristopherRandles i see that's a bit odd but I am not betting there only here, but I agree it is cheap

both the dynamic model predictions, medium and long range suggest the highest bin ; the pure statistical (arimax) model is very sensitive so it did shift the mean temp down now a bit lower by one bin recently, but most of the probability mass is by far still in the highest bin -- its the most conservative estimate I have and I still am betting much more conservatively than it suggests based on the shifting trend, and how many future chances there are to update