Figure 8. A scatter diagram of hourly temperature and
CO2 concentration levels at BRW, 1 Jan 1985 – 31 Dec
2015
The autocorrelative nature of hourly temperature is an important
characteristic of the data (Figure 9). As the figure indicates, the
magnitude and the duration of the autocorrelative process are
significant. In terms of magnitude, the estimated one-hour
autocorrelation in temperature equals 0.9970, a value that is so large
that it is reasonable to wonder if there is a unit root issue. If this
is indeed the case, the results of this study could be spurious for the
reasons explained by Kennedy ( 2008, p. 301).
Fortunately, an Augmented Dickey-Fuller test yields a P -value
that is less than 0.0001 both with and without a possible trend, and
thus the null hypothesis of a unit root is rejected. Consistent with
this finding, the Phillips-Perron test for a unit root also yields aP -value less than 0.0001 both with and without a possible trend.
Consideration was given to further unit root testing using the DF-GLS
test developed by Elliot et al. (1996). This test is regarded as a
leading “second-generation” unit root test that avoids some of the
shortcomings of the Augmented Dickey-Fuller and Phillips-Perron tests
(Baum and Hurn, 2021, pp. 117-120 ). The application of this methodology
requires a data series without any gaps. The Barrow data set has 325
gaps in terms of temperature, and thus, the DF-GLS test cannot be
applied.
Fortunately, hourly temperature data analysis at another observatory in
the polar region may be instructive. One of the few stations in the
polar region that substantially meets the zero data gap requirements of
the DF-GLS test is the Syowa station on East Ongle Island, located about
4km from the Antarctic continent with a latitude 69.0125° South and a
longitude of 39.5900° East. This station is supported by the National
Institute of Polar Research in Japan. The data from this station was
obtained from NASA’s CERES/ARM Validation Experiment (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/SYN1degEd41Selection.jsp).
From 14 Apr 2002 through 31 Jan 2016, a period with 120,982 hours and no
data gaps, the mean temperature at the Syowa Observatory was about -10.7
°C, with the hourly values ranging from 41.25 °C to 7.65 °C. At one hour
lagged, the autocorrelation in temperature equals 0.9959, a value
seemingly suggestive of a unit root issue. This possible suspicion is
not supported by the Augmented Dickey-Fuller, Phillips–Perron, or the
DF-GLS tests.
While the available tests do not support the null hypothesis of a unit
root in the hourly temperature data, a quantitative analysis of hourly
time-series temperature data needs to control its time-series nature to
effectively extract the signal from the noise in the data. The method of
ordinary least squares is woefully deficient in this regard. This point
is consistent with a warning by Granger and Newbold (1974, p. 117), who
note the following: “In our opinion the econometrician can no longer
ignore the time series properties of the variables with which he is
concerned ‐ except at his [ or her ] peril.” The consequences of
ignoring their warning include inefficient estimates of the regression
coefficients, suboptimal forecasts, and invalid tests of statistical
significance. Unfortunately, an inspection of “Statistical Methods in
the Atmospheric Sciences,” authored by Wilks (2019), suggests that this
warning has not been fully heeded in the atmospheric sciences.