Time series analysis and forecasting of carbon dioxide counts in Alarm, Northern Territories for the year 2005, projected from climate data from prior years.

1. Data Analysis
Measurements taken over the last ten years (Jan. 1994 to Dec. 2004) have shown a steady increase in
atmospheric CO2 concentration, fluctuating throughout the year. A brief analysis of the sample data
shows acceptable normality (Shapiro-Wilk’s W = 0.98523, p-value = 0.1652), so forecasts for the coming
years should be reliable. After removing the deterministic components of the data, residuals were
stationary (Dickey-Fuller = -5.72, p-value = 0.01;
KPSS = 0.016, p-value = 0.1) and followed an
invertible MA(1) process (𝜃̂ = -0.5601, SE =
0.0821). Once the process the residuals follow
was identified, values for the next 24 months
were forecasted and tested for any remaining
dependence using ACF and PACF plots and a
Box-Ljung test, which found no remaining
dependence (Box-Ljung 𝜒24
2
= 18.964, p-value =
0.7539) Adding the deterministic elements back
to the expected values of the process for the
next twenty-four months yielded our expected
CO2 levels for the next two years, illustrated in
the graph to the left. Point estimates and 95%
confidence intervals for the year of 2005 are
given below.
Month Estimate
95% CI
Lower
95% CI
Upper
Jan-05 382.13 380.46 383.10
Feb-05 382.56 381.05 384.07
Mar-05 383.05 381.54 384.56
Apr-05 383.44 381.93 384.95
May-05 381.37 379.86 382.88
Jun-05 374.93 373.42 376.44
Jul-05 368.99 367.48 370.50
Aug-05 369.58 368.07 371.09
Sep-05 374.55 373.04 376.06
Oct-05 378.89 377.38 380.40
Nov-05 381.68 380.17 383.19
Dec-05 383.30 381.79 384.81