# Do Central Park's ten hottest days reveal warming more clearly?

## Result

No. For the 35 complete years from 1991 through 2025, allowing for correlation between years and using an outlier-resistant trend estimate strengthens rather than reverses the original comparison.

The annual mean temperature has an ordinary least-squares slope of **+0.305 °C per decade**. A Newey–West heteroskedasticity-and-autocorrelation-consistent calculation with three lags gives a 95% confidence interval of **+0.159 to +0.452 °C per decade** (two-sided p = 0.00005). The Theil–Sen median slope is **+0.323 °C per decade**, with a 95% confidence interval of **+0.059 to +0.550 °C per decade**.

For the mean of each year's ten highest daily maximum temperatures, the ordinary least-squares slope is **−0.164 °C per decade**. Its Newey–West 95% confidence interval is **−0.451 to +0.123 °C per decade** (p = 0.264). The Theil–Sen estimate is **−0.241 °C per decade**, with a 95% confidence interval of **−0.736 to +0.400 °C per decade**. Both intervals include zero.

## Interpretation

The comparison therefore holds under both checks. The annual mean has a clearly positive trend, while the hottest-ten-days series has no detectable trend and substantially more interannual noise. This does not establish cooling of hot extremes: the negative estimates are imprecise and compatible with zero or modest warming.

The residual lag-one correlations are −0.089 for annual means and −0.324 for the hot-ten series; Durbin–Watson statistics are 2.01 and 2.55, respectively. Newey–West inference was used regardless, so standard errors do not require independent, constant-variance residuals up to the selected three-year lag window. Theil–Sen estimates the median of pairwise slopes and is less sensitive than least squares to unusual years.

## Data and completeness

The source is NOAA GHCN-Daily station USW00094728, New York City Central Park. The station file contains TMAX and TMIN but not TAVG, so daily mean temperature is calculated as (TMAX + TMIN) / 2, following the GHCN-Daily documentation. Temperatures are stored by NOAA in tenths of degrees Celsius.

A year qualifies only if it has exactly 365 or 366 dates, with nonmissing TMAX and TMIN and blank NOAA quality flags on every date. All years 1991–2025 pass. The partial 2026 record is excluded. The package records the retrieval timestamp, server modification dates, ETags, the raw-file SHA-256 digest, and year-level quality checks.

## Limitations

This conclusion is specific to Central Park and 1991–2025. It should not be generalized to New York State, other stations, or hot extremes generally. The record is from one urban station; site history, instruments, observation practices, land-cover change, and homogenization can affect trends. (TMAX + TMIN) / 2 is not a true 24-hour mean. The result can also depend on the extreme definition: percentile thresholds, consecutive heat-wave days, seasonal metrics, nighttime minima, or a different number of hottest days may behave differently.

Newey–West intervals are asymptotic and the sample contains only 35 years. The three-lag bandwidth is a standard automatic choice, not a physical model of climate persistence. Theil–Sen is robust to outliers but does not solve possible station inhomogeneity or nonlinear change. No causal attribution is attempted.

## Conclusion

At Central Park during 1991–2025, the annual mean reveals warming more clearly than the ten hottest daily maxima. That finding survives autocorrelation-robust inference and a robust median-slope estimator.
