Statistical analysis and time-series models for minimum/maximum temperatures in the Antarctic Peninsula

Abstract

Our object in this paper is to study the temperature variations in the Antarctic Peninsula using multiple regression models with correlated errors admitting ARMA models with nonGaussian innovations. We found that the fitted models adequately describe the variations. The data we consider are minimum/maximum monthly temperatures recorded at the Faraday station by the British Antarctic Survey for the period from January 1951 to December 1995. The time series models considered here are novel in the sense that the linear ARMA models have innovations which have extreme value distributions, and the maximum likelihood estimation described here can be widely used in many disciplines.The time series models we fitted indicate that the mean of the minimum temperatures is likely to increase over the next 50 years and the temperatures will be above 0 o C during the summer months which means that the melting season will increase, creating more climatic and ecological problems. Although the mean temperature is reported to have increased by 2.5 o C we believe that the maximum temperatures have remained unchanged over the past 45 years. This has led to a decrease in the diurnal temperature range which has also been observed in many other parts of the globe.The influence of human activity on climate is still unknown but our ability to perturb the ozone layer is an established fact. We established a relationship between minimum monthly temperatures and ozone levels and found they are highly negatively correlated (at a lag of one month) implying that the higher levels of ozone in the air keep temperatures low. This resulted in a new time series model relating the minimum temperatures to ozone levels. After appropriate statistical tests, we have come to the conclusion that the observed increase in the minimum temperatures is a consequence of human activity rather than natural causes and so a reduction in the production of "greenhouse gases" could lead to a decrease in minimum temperatures, thereby reducing the adverse effect of global warming in the Antarctic Peninsula.

On multivariate nonlinear regression models with stationary correlated errors

“…The results are somewhat similar to those reported by Hughes et al (2006), where they assumed that the errors are correlated and Gaussian. However, there is some difference in the estimates (and their standard errors) when they fitted a linear model with converse extreme value distribution.…”

“…Therefore the methodology we developed in this paper is very appropriate and we use the model and analysis suggested in Section 4.3. Since it is widely believed that the ozone levels in the Antarctica have an affect on temperatures (see Hughes et al, 2006), we include this as our third explanatory variable (Fig. 3).…”

“…In view of this, it is obvious that their methodology does not lead to good estimates. Recently Hughes et al (2006), have considered the monthly minimum/maximum temperatures observed during January 1951-December 2004 and they have analyzed the data using linear time series models where the innovations have extreme value distributions. They conclude that there is a significant increase in minimum temperatures, but the increase is not statistically significant in the time-series on maximum temperatures.…”

“…The second example we consider is the minimum and maximum monthly temperatures (and ozone levels) observed at a station in the Antarctic Peninsula and these data are considered to illustrate our methodology where the regression model is linear. For a different analysis of these temperature data, we refer to a recent paper by Hughes et al (2006), referred to as HSS from now on.…”

Generalized extreme value distribution with time-dependence using the AR and MA models in state space form

“…by Hughes et al (2007), however, they develop a linear time series model using an ARMA representation with innovations following the extreme value distribution.…”