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

It is now widely known that Antarctic air is warming faster than
the rest of the world, and the Antarctic peninsula has experienced
major warming over the last 50 years. The monthly mean near
surface temperature at the Faraday/Vernadsky station has increased
considerably, at a rate of 0.56 degrees C per decade over the
year and at 1.09 degrees C per decade over the winter. The increase
is not the same over all the stations in the Antarctic region,
and the increase is very significant at the Faraday/Verdansky station.
Only at this station are the minimum/maximum monthly temperatures,
for the period $1951-2004$, separately available, and we
believe that the increase
in mean surface temperature at this station is mainly due to the
increases in minimum temperatures.
Therefore our
object in this paper is to study the variations in the min/max
temperatures using a multiple regression model with non-Gaussian
correlated errors. By separately analysing the minimum
and maximum temperatures we could clearly identify the source of increase.
The average temperature (usually calculated as (max+min)/2) smooths
out the variation, and may not be that informative.
We model the correlated errors using a linear
Autoregressive Moving Average model with innovations
which have an extreme value distribution. We describe the maximum
likelihood estimation methodology and apply this to the data sets
described above. The methods proposed here can be widely used in
other disciplines as well.

Our analysis has shown that the increase in the minimum
monthly temperatures
is approximately 6 degrees C over 53 years (1951-2003), whereas
we did not find any significant change in
the maximum temperature over the same period.

We also establish a relationship between the minimum monthly temperatures
and ozone levels. We use these models, fitted upto December 2003,
to obtain monthly forecasts for the year 2004 and compare it with the true
values available upto December 2004.

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