1. An Assessment of Climate Change

3. But there remain issues about the data.
The key problem is one of data and whether the data is reliable. This is because everyone uses the data and all judgements of the computer models must rest on how well they predict the data.
But there remain issues about the data.

4. There have been many critics of the massaging of the temperature data.
Long Run Data -- ice cores, tree rings, principal components, etc.
Short Run Data – urban heat islands, bias corrections, choice of mean, etc.
There have been many critics of the massaging of the temperature data.

5. Global Temperature Anomalies
The global mean surface air temperature for that period was estimated to be 14°C (57°F), with an uncertainty of several tenths of a degree.

6. CO2 Atmospheric Concentration in Parts Per Million (Million)

9. Note that this time series model (ARMAX) fits the data well and predicts that in about 33 years the temperature of the earth will rise about 1o C or 3o C in 100 years, assuming that CO2 concentration continues to grow at the 2000 – 2016 rate. There is no physical modeling or computer simulation. This is a straightforward time series forecast using monthly CO2 and temperature data from 1965 to 2016.

10. Do Economic Activities Significantly Cause Growth in CO2 Concentrations?

12. Step 1: testing for a unit root in l_CO2
Augmented Dickey-Fuller test for l_CO2
including one lag of (1-L)l_CO2
sample size 24
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) e
estimated value of (a - 1):
test statistic: tau_c(1) =
asymptotic p-value
1st-order autocorrelation coeff. for e:
Step 2: testing for a unit root in l_WorldGDP
Augmented Dickey-Fuller test for l_WorldGDP
including one lag of (1-L)l_WorldGDP
sample size 24
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) e
estimated value of (a - 1):
test statistic: tau_c(1) =
asymptotic p-value
1st-order autocorrelation coeff. for e:

13. Step 3: cointegrating regression
OLS, using observations (T = 26)
Dependent variable: l_CO2
coefficient std. error t-ratio p-value
const e-019 ***
l_WorldGDP e-032 ***
Mean dependent var S.D. dependent var
Sum squared resid S.E. of regression
R-squared Adjusted R-squared
Log-likelihood Akaike criterion −
Schwarz criterion − Hannan-Quinn −
rho Durbin-Watson
Step 4: testing for a unit root in uhat
Augmented Dickey-Fuller test for uhat
including one lag of (1-L)uhat
sample size 24
unit-root null hypothesis: a = 1
model: (1-L)y = (a-1)*y(-1) e
estimated value of (a - 1):
test statistic: tau_c(2) =
asymptotic p-value
1st-order autocorrelation coeff. for e: 0.057
There is evidence for a cointegrating relationship if:
The unit-root hypothesis is not rejected for the
individual variables, and (b) the unit-root hypothesis
is rejected for the residuals (uhat) from the cointegrating regression.

14. Model 3: Error Correction OLS, using observations 1991-2015 (T = 25)
Dependent variable: d_l_CO2
coefficient std. error t-ratio p-value
const ***
d_l_WorldGDP
uhat_ − −
Mean dependent var S.D. dependent var
Sum squared resid S.E. of regression
R-squared Adjusted R-squared
F(2, 22) P-value(F)
Log-likelihood Akaike criterion −
Schwarz criterion − Hannan-Quinn −
rho Durbin-Watson
About ¼ of the CO2 growth is due to GDP growth, if we accept the estimates to the left. But, statistically speaking the null of 0% cannot be rejected at the standard 1%, 5% , or 10% significance levels. To stabilize CO2 levels we would need a 10% fall in world GDP, ceteris paribus. This seems extreme and unacceptable.

16. Temporal Ordering is from Black (Temp) to Light Gray (CO2)