Detection and Attribution of Climate Change Through Econometric Methods (Figures)

.6 2.0 .4 1.6 .2 1.2 W/m2 ºC Figures .0 -.2 0.4 -.4 0.0 -.6 1880 a) 0.8 1900 1920 1940 1960 1980 2000 -0.4 1880 b) .4 1900 1920 1940 1960 1980 2000 .8 .3 .6 .2 .4 .1 .2 ºC ºC .0 -.1 .0 -.2 -.2 -.3 -.4 -.4 -.5 1880 c) 1900 1920 1940 1960 1980 2000 -.6 1880 d) .8 .4 .6 .3 .4 1900 1920 1940 1960 1980 2000 .2 .2 ºC ºC .1 .0 .0 -.2 -.1 -.4 -.2 -.6 -.8 1890 1910 1930 1950 1970 1990 -.3 1880 2010 1900 1920 1940 1960 1980 2000 e) f) Figure 1. Global temperatures (filtered; panel a), TRF (panel b), AMO (panel c), Temp_TSB (panel d), Temp_DS (panel e) and Temp_S (panel f). 1. 2 1. 5 0. 8 1. 0 0. 4 ºC ºC 0. 5 0. 0 0. 0 -0. 4 -0. 5 -0. 8 -1. 2 1880 1900 1920 1940 1960 DS _1 DS _2 1980 2000 -1. 0 1880 1900 1920 1940 1960 1980 2000 DS _3 DS _4 Figure 2. Cointegrated (panel a) and not cointegrated (panel b) simulated difference stationary series. Tables Table 1. Standard unit root/trend stationary tests applied to G, TRF and simulated temperature series Temp_TSB, Temp_DS and Temp_S. Series ADF DF-GLS KPSS ERS-PO Ng-Perron G -2.79 (3) -2.68 (3) 0.26 (8) 7.18 (3) -5.47[MZa] ; -1.64[MZt] ; 0.30[MSB] ; 16.61[MP T ] (8) TRF -2.73 (12) -2.21 (11) 0.32 (9) 0.10 (12) -6.51[MZa] ; -1.71[MZt] ; 0.26[MSB] ; 14.04[MP T ] (9) AMO -3.31 (2) -2.45 (2) 0.10 (9) 2.16 (2) -7.09 [MZa] ; -1.83 [MZt] ; 0.26 [MSB] ; 3.66 [MP T ] (4) Temp_TSB -2.60 (2) -2.43 (2) 0.25 (8) 8.70 (2) -8.26[MZa] ; -1.85[MZt] ; 0.22[MSB] ; 11.61[MP T ] (3) Temp_DS -2.93 (0) -1.97 (0) 0.21 (9) 14.16 (0) -6.63[MZa] ; -1.73[MZt] ; 0.26[MSB] ; 13.80[MP T ] (1) Temp_S -4.92 (0) -4.81 (0) 0.10 (7) 0.79 (0) -28.46[MZa] ; -3.75[MZt] ; 0.13[MSB] ; 0.93[MP T ] (4) The model specification includes a constant and a trend, with the exception of AMO and Temp_S for which only a constant term is included. The lag length and bandwidth shown in parenthesis. Figures in bold and italics indicate that the statistic is significant at the 5% and 10% levels, respectively. For the ADF and DF-GLS tests the lag length was selected via the Akaike Information Criterion. For the KPSS test, the Bartlett kernel is used with the bandwidth selected using the Newey-West method. For the ERS-PO, the autoregressive spectral density estimator is used with the lag length selected via the Akaike Information Criterion. For the Ng-Perron tests, the long-run varaince is estimated using an autoregressive spectral density estimation method with GLS-detrended and the lag length was selected via the Modified Akaike Information Criterion. Table 2. Perron-Yabu test applied G, TRF and simulated temperature series Temp_TSB, Temp_DS and Temp_S. Series Exp-Wald statistic value G 12.34 TRF 7.92 AMO 0.28 Temp_TSB 19.50 Temp_DS 0.15 Temp_S -0.31 Bold figures denote statistical significance at the 1% level. Table 3. Tests for a unit root allowing for a one-time break in the trend function applied to filtered G, TRF and simulated temperature series Temp_TSB. Series Tb k µ β γ α tα tα λAO tr G 1956 0 -0.27 (-15.94) 0.0031 (9.01) 0.0063 (8.28) 0.34 -7.98a -7.30a TRF 1960 1 -0.09 (-5.34) 0.0064 (20.82) 0.0221 (28.98) 0.84 -4.58a -4.11b Temp_TSB 1978 0 -0.34 (-18.61) 0.0040 (13.20) 0.0129 (9.51) 0.31 -8.17a -7.79a The regression model for the unit root tests is defined in regression (6). The symbols used are defined as follows: Tb is the estimate of the break date; k is the number of lagged differences added to correct for serial autocorrelation; µ, β and γ are the regression coefficients of the trend function and the corresponding t-statistic values are shown in parenthesis. Bold numbers denote statistical significance at the 5% levels. α is the estimate of the sum of the autoregressive coefficients and tα is the Perron (1997) unit root test statistic. tα λAO is the Kim-Perron (Kim tr and Perron, 2009) unit root test statistic. a, b denote statistical significance at the 1% and 5% levels, respectively. Table 4. Cointegration tests applied to simulated variables DS_1 and DS_2, and DS_3 and DS_4. Series Trace statistic Max-eigenvalue statistic Engle-Granger ADF test statistic DS_1, DS_2 27.91 27.11 -11.61 DS_3, DS_4 4.25 3.77 -1.70 Bold numbers denote statistical significance at the 1% level. Table 5. Test for nonlinear co-trending between filtered G and TRF. r Test statistic 10% critical region 5% critical region 1 0.07 >0.12 >0.15 2 0.32 >0.17 >0.20 Bold numbers denote statistical significance at the 10% level.