Evidence of Causality between the Atmospheric Concentration Level of - PowerPoint PPT Presentation

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 37 th IAEE International Conference New York, New York June 2014

The Approach of this Paper This paper addresses the issue of causality between CO 2 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 X t. If some other series Y t , contains information in past terms that helps in the prediction of X t and if this information is contained in no other series used in the predictor, then Y t is said to cause X t .” [Granger, 1969, p 430]. This study embraces Granger’s view of causality by examining • whether lagged values of CO 2 lead to more accurate forecasts of temperature.

The Approach of this Paper (Continued) The analysis makes use of lagged hourly CO 2 atmospheric • concentration data from the Mauna Loa Observatory (MLO) in Hawaii, data on the hourly temperature at the nearby Hilo international Airpor t, 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 CO 2 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 CO 2 -augmented forecasts are based on an econometrically estimated equation whose residual error terms have the property of white noise.

Data Sources • The hourly CO 2 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 • CO 2 concentrations have a seasonal and diurnal pattern

Day-Ahead Temperature Forecast Accuracy at the Hilo Location by Month The RMSE in NOAA’s The RMSE in Forecast ( 0 C) CustomWeather’s Forecast ( 0 C) 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 CO 2 Concentration Levels at MLO, 7 August 2009 – 30 June 2011.

Exploiting the Diurnal Nature of the Variation in CO 2 • Establishing causality requires the use of lagged CO 2 values • The CO 2 concentration level in hour t – 24 is used as an explanatory variable. • This variable is highly correlated with the CO 2 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 o C. • CustomWeather’s forecast over the same period has a RMSE of 1.371 o C.

Actual Temperature at the Hilo International Airport and CustomWeather’s Day-Ahead Temperature Forecast, 1 July – 31 December 2011 45 o 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 CFH 3 is equal to zero

• The first structural forecast is more accurate than CustomWeather’s. • The structural forecast that excludes CFH 3 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 CFH 3 , 1 July – 31 December 2011. 45 o line

Conclusion • The out-of-sample results are consistent with causality between CO 2 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 CO 2 concentration level, whose contribution to temperature is consistent with scientific principles, but one which is somehow ignored by leading meteorologists.