11 Spurious Correlation

11.1 Trending Variables

Tambonthongchai

THE SOURCE DATA SHOW A STRONG STATISTICALLY SIGNIFICANT CORRELATION OF CORR=0.75 BETWEEN ANNUAL CHANGES IN MLO CO2 AND ANNUAL EMISSIONS. THIS CORRELATION APPEARS TO SUPPORT THE USUAL ASSUMPTION THAT CHANGES IN ATMOSPHERIC CO2 CONCENTRATION ARE CAUSED BY FOSSIL FUEL EMISSIONS AND THAT THEREFORE THESE CHANGES CAN BE MODERATED WITH CLIMATE ACTION TO CONTROL AND REDUCE THE RATE OF WARMING.

HOWEVER, IT IS KNOWN THAT SOURCE DATA CORRELATION BETWEEN TIME SERIES DATA DERIVE FROM TWO SOURCES. THESE ARE (1) SHARED TRENDS WITH NO CAUSATION IMPLICATION AND (2) RESPONSIVENESS AT THE TIME SCALE OF INTEREST. HERE THE TIME SCALE OF INTEREST IS ANNUAL BECAUSE THE THEORY REQUIRES THAT ANNUAL CHANGES IN ATMOSPHERIC CO2 CONCENTRATION ARE CAUSED BY ANNUAL FOSSIL FUEL EMISSIONS. THIS TEST IS MADE BY REMOVING THE SHARED TREND THAT IS KNOWN TO HAVE NO CAUSATION INFORMATION OR IMPLICATION. HERE WE FIND THAT WHEN THE SHARED TREND IS REMOVED THE OBSERVED CORRELATION DISAPPPEARS. THE APPARENT CORRELATION BETWEEN EMISSIONS AND CHANGES IN ATMOSPHERIC CO2 CONCENTRATION IS THUS FOUND TO BE SPURIOUS.

THE DATA FOR ANNUAL FOSSIL FUEL EMISSIONS AND ANNUAL CHANGES IN ATMOSPHERIC CO2 CONCENTRATION DO NOT SHOW THAT FOSSIL FUEL EMISSIONS CAUSE ATMOSPHERIC CO2 CONCENTRATION TO CHANGE. THE FINDING IMPLIES THAT THERE IS NO EMPIRICAL EVIDENCE IN SUPPORT OF THE THEORY OF CLIMATE ACTION. THIS THEORY HOLDS THAT MOVING THE GLOBAL ENERGY INFRASTRUCTURE FROM FOSSIL FUELS TO RENEWABLES WILL MODERATE THE RATE OF INCREASE IN ATMOSPHERIC CO2 AND THEREBY MODERATE THE RATE OF WARMING.

Tambonthongchai: Climate Data Case (via Arve)

Munshi Abstract

Abstract: Unrelated time series data can show spurious correlations by virtue of a shared drift in the long term trend. The spuriousness of such correlations is demonstrated with examples. The SP500 stock market index, GDP at current prices for the USA, and the number of homicides in England and Wales in the sample period 1968 to 2002 are used for this demonstration. Detrended analysis shows the expected result that at an annual time scale the GDP and SP500 series are related and that neither of these time series is related to the homicide series. Correlations between the source data and those between cumulative values show spurious correlations of the two financial time series with the homicide series. These results have implications for empirical evidence that attributes changes in temperature and carbon dioxide levels in the surface-atmosphere system to fossil fuel emissions

Munshi Memo

Spurious correlations of this nature are sometimes found in published research. For example, climate science attributes the rise in atmospheric carbon dioxide to fossil fuel emissions and cites correlations between the data as empirical evidence (IPCC, 2007) (IPCC, 2014) (Canadell, 2007) (Kheshgi, 2005). Detrended analysis shows that correlations between emissions and atmospheric CO2 and oceanic CO2 are spurious because they disappear when the data are detrended (Munshi, Responsiveness of Atmospheric CO2 to Anthropogenic Emissions, 2015) (Munshi, Fossil Fuel Emissions and Ocean Acidification, 2015). These anomalous results likely derive from large and perhaps unquantifiable uncertainties in natural flows of carbon dioxide in the surface-atmosphere system (Munshi, Uncertain Flow Accounting and the IPCC Carbon Budget, 2015).

Munshi (2016) Spurious Correlations in Time Series Data: A Note [(pdf)[pdf/Munshi_2016_Spurious_Time_Series.pdf)

Munshi Abstract

A statistically significant correlation between annual anthropogenic CO2 emissions and the annual rate of accumulation of CO2 in the atmosphere over a 53-year sample period from 1959-2011 is likely to be spurious because it vanishes when the two series are detrended. The results do not indicate a measurable year to year effect of annual anthropogenic emissions on the annual rate of CO2 accumulation in the atmosphere.

Munshi 82015) Spurious Anthropogenic CO2 (pdf)

Wu Abstract

This paper examines three types of spurious regressions where both the dependent and independent variables contain deterministic trends, stochastic trends, or breaking trends. We show that the problem of spurious regression disappears if the trend functions are included as additional regressors. In the presence of autocorrelation, we show that using a Feasible General Least Square (FGLS) estimator can help alleviate or eliminate the problem. Our theoretical results are clearly reflected in finite samples. As an illustration, we apply our methods to revisit the seminal study of Yule (1926).

Wu (2007) On spurious regressions with trending variables (pdf)