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Evidence of Causality between the Atmospheric Concentration Level of Carbon Dioxide and Temperature

Kevin F. Forbes School of Business and Economics The Catholic University of America Washington, DC Forbes@CUA.edu 37th IAEE International Conference New York, New York June 2014

The Approach of this Paper

• This paper addresses the issue of causality between CO2 and

temperature by following Granger [1969], who defined causality in terms of whether lagged values of a variable lead to more accurate predictions of some other variable.

• In his words, “The definition of causality …is based entirely on the

predictability of the some series, say Xt. If some other series Yt , contains information in past terms that helps in the prediction of Xt and if this information is contained in no other series used in the predictor, then Yt is said to cause Xt.” [Granger, 1969, p 430].

• This study embraces Granger’s view of causality by examining

whether lagged values of CO2 lead to more accurate forecasts of temperature.

The Approach of this Paper (Continued)

• The analysis makes use of lagged hourly CO2 atmospheric

concentration data from the Mauna Loa Observatory (MLO) in Hawaii, data on the hourly temperature at the nearby Hilo international Airport, and day-ahead hourly forecast data for the Hilo location.

• The day-ahead hourly forecast variables are included to control for

confounding influences. They are also included to model their possible interactions with the CO2 variable.

• The estimated equation is used to make hourly out-of-sample

forecasts for a six month period. Consistent with Granger’s definition of causality, the CO2-augmented forecasts are based on an econometrically estimated equation whose residual error terms have the property of white noise.

Data Sources

• The hourly CO2 data were obtained from

NOAA’ Earth System Research Laboratory.

• The hourly temperature data were obtained

from NOAA

• The forecast data were obtained from

CustomWeather, a San Francisco based weather forecasting firm that generates forecasts for approximately 70,000 locations in 200 countries.

Attributes of the Data

• There is some evidence that

CustomWeather’s forecasts for the Hilo location are more accurate than NOAA’s

• CO2 concentrations have a seasonal and

diurnal pattern

Day-Ahead Temperature Forecast Accuracy at the Hilo Location by Month

The RMSE in NOAA’s Forecast (0C) The RMSE in CustomWeather’s Forecast (0C) July 2011 ~1.8 1.2 August 2011 ~2.0 1.3 September 2011 ~1.5 1.5 October 2011 ~1.2 1.3 November 2011 ~1.6 1.4 December 2011 ~2.4 1.5

The Autocorrelations in the Hourly CO2 Concentration Levels at MLO, 7 August 2009 – 30 June 2011.

Exploiting the Diurnal Nature of the Variation in CO2

• Establishing causality requires the use of

lagged CO2 values

• The CO2 concentration level in hour t – 24 is

used as an explanatory variable.

• This variable is highly correlated with the CO2

level in hour t but is obviously itself unaffected by the temperature in period t.

A Multivariate Model of Temperature

Explanatory Variables

More Variables…

More Variables…

Econometric Issues

• Functional Form: Though the relationships

are highly unlikely to be strictly linear, there is no basis, theoretical or otherwise, to assume any particular nonlinear form.

• ARMA disturbances: Time series regressions

using high frequency data are often plagued by autoregressive error structures that are not easily accommodated using standard AR(p) methods.

Functional Form

The model was estimated using the multivariable fractional polynomial (MFP) model. This is a useful technique when one suspects that some or all of the relationships between the dependent variable and the explanatory variables are non-linear (Royston and Altman, 2008), but there is little or no basis, theoretical or otherwise, on which to select particular functional forms.

Results of the MFP Analysis

Modeling the ARMA Disturbances

• The OLS residuals do not have the property of white noise.
• To remedy the problem with the residuals, the equation was re-estimated by

modeling an ARMA process. The modeling process proceeds by specifying both the autoregressive (AR(p)) and moving average (MA(q)) characteristics of the error structure.

• AR(p): The modeled lag lengths are p = 1, 2, 3, 4, 24, 48, 72, 96, 120, 144,

168, 192, 216, 240, 275, 312, 336, 360, and 384.

• MA(q): The modeled lag lengths are q = 1, 2, 3, 4, 5, 6, 7, 8, 9, 17,18, 19,

20, 21, 22, 23, 24, 25, 26,27, 43, 47, 48, 53, 69, 70, 72, 74, 77, 79, 87, 92, 93, 100, 101, 103, 107, 118, 120, 122, 123, 132, 137, 138, 139, 140, 144, 159, 168, 185, 189, 209, 241, 243, 260, 410, 595, 600, 681, 750, 784, and 794

Residual Autocorrelations After ARMA Estimation

Estimation Results

Out-of-Sample Results

• The ARMA parameter estimates were used to

produce an out-of-sample dynamic forecast from 1 July 2011 to 31 December 2011.

• The dynamic forecast has a RMSE of 0.771 oC.
• CustomWeather’s forecast over the same

period has a RMSE of 1.371 oC.

Actual Temperature at the Hilo International Airport and CustomWeather’s Day-Ahead Temperature Forecast, 1 July – 31 December 2011

45o line

Actual Temperature at the Hilo International Airport and an ARMA-based Dynamic Temperature Forecast, 1 July – 31 December 2011

Out-of-Sample Structural Forecasts

• A structural forecast does not consider the

estimated ARMA terms

• Two structural forecasts were calculated
• The first structural forecast considers all the

estimated coefficients exclusive of the ARMA terms

• The second structural forecast assumes that

the coefficient corresponding to CFH3 is equal to zero

• The first structural forecast is more accurate

than CustomWeather’s.

• The structural forecast that excludes CFH3 has

a very large RMSE. It is also severely biased in the sense that it underestimates temperature.

Actual Temperature at the Hilo International Airport and an ARMA-based Structural Temperature Forecast, 1 July – 31 December 2011

Actual Temperature at the Hilo International Airport and an ARMA-based Structural Temperature Forecast that Excludes the Estimated Effect of CFH3, 1 July – 31 December 2011.

45o line

Conclusion

• The out-of-sample results are consistent with causality

between CO2 and temperature.

• In the absence of methodological and/or data issues,

the only other explanation for the reported results is that there is an omitted relevant explanatory variable.

• Such a variable would need to be one that is highly

correlated with the CO2 concentration level, whose contribution to temperature is consistent with scientific principles, but one which is somehow ignored by leading meteorologists.