Table A1

Bounds test for co-integration relationship (closing price)

Critical value bounds of the F-statistic: Intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 15.16445*** 
Critical value bounds of the F-statistic: Intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 15.16445*** 
View large
Table A2

Model criteria/goodness of fit (closing price)

StatisticValueStatisticValue
R-squared 0.937704 Mean dependent var 6,907.006 
Adjusted R-squared 0.936255 S.D. dependent var 329.4274 
S.E. of regression 83.17276 Akaike info criterion 11.70756 
Sum squared resid 1,189,846 Schwarz criterion 11.79728 
Log likelihood −1031.119 Hannan–Quinn criterion 11.74395 
F-statistic 647.2555 Durbin–Watson stat 2.003219 
Prob(F-statistic) 0.000000  
StatisticValueStatisticValue
R-squared 0.937704 Mean dependent var 6,907.006 
Adjusted R-squared 0.936255 S.D. dependent var 329.4274 
S.E. of regression 83.17276 Akaike info criterion 11.70756 
Sum squared resid 1,189,846 Schwarz criterion 11.79728 
Log likelihood −1031.119 Hannan–Quinn criterion 11.74395 
F-statistic 647.2555 Durbin–Watson stat 2.003219 
Prob(F-statistic) 0.000000  
View large
Table A3

Autocorrelation test (closing price)

ACPACQ-StatProb*
1 −0.013 −0.013 0.0327 0.856 
2 −0.071 −0.071 0.9406 0.625 
3 −0.033 −0.035 1.1386 0.768 
4 0.107 0.102 3.2420 0.518 
5 −0.022 −0.024 3.3320 0.649 
6 −0.049 −0.037 3.7706 0.708 
ACPACQ-StatProb*
1 −0.013 −0.013 0.0327 0.856 
2 −0.071 −0.071 0.9406 0.625 
3 −0.033 −0.035 1.1386 0.768 
4 0.107 0.102 3.2420 0.518 
5 −0.022 −0.024 3.3320 0.649 
6 −0.049 −0.037 3.7706 0.708 
View large
Table A4

Bounds test for co-integration relationship (EUR/GBP)

Critical value bounds of the F-statistic: intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 30.7909*** 
Critical value bounds of the F-statistic: intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 30.7909*** 
View large
Table A5

Model criteria/goodness of fit (EUR/GBP)

StatisticValueStatisticValue
R-squared 0.377874 Mean dependent var 0.855048 
Adjusted R-squared 0.367147 S.D. dependent var 0.018020 
S.E. of regression 0.014335 Akaike info criterion −5.630011 
Sum squared resid 0.035756 Schwarz criterion −5.558511 
Log likelihood 505.0710 Hannan–Quinn criterion −5.601016 
F-statistic 35.22865 Durbin–Watson stat 2.022121 
Prob(F-statistic) 0.000000   
StatisticValueStatisticValue
R-squared 0.377874 Mean dependent var 0.855048 
Adjusted R-squared 0.367147 S.D. dependent var 0.018020 
S.E. of regression 0.014335 Akaike info criterion −5.630011 
Sum squared resid 0.035756 Schwarz criterion −5.558511 
Log likelihood 505.0710 Hannan–Quinn criterion −5.601016 
F-statistic 35.22865 Durbin–Watson stat 2.022121 
Prob(F-statistic) 0.000000   
View large
Table A6

Autocorrelation test (EUR/GBP)

ACPACQ-StatProb*
1 0.157 0.157 4.4710 0.034 
2 −0.102 −0.130 6.3650 0.041 
3 −0.097 −0.061 8.0967 0.044 
4 0.033 0.049 8.2972 0.081 
5 −0.055 −0.091 8.8564 0.115 
6 −0.064 −0.039 9.6155 0.142 
ACPACQ-StatProb*
1 0.157 0.157 4.4710 0.034 
2 −0.102 −0.130 6.3650 0.041 
3 −0.097 −0.061 8.0967 0.044 
4 0.033 0.049 8.2972 0.081 
5 −0.055 −0.091 8.8564 0.115 
6 −0.064 −0.039 9.6155 0.142 
View large
Table A7

Bounds test for co-integration relationship (USD/GBP)

Critical value bounds of the F-statistic: Intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 2.0678 
Critical value bounds of the F-statistic: Intercept and no trend (case II)
K90% level95% level99% level
7 I(0) I(1) I(0) I(1) I(0) I(1) 
5.59 6.26 6.56 7.3 8.74 9.63 
 Calculated F-Statistic 2.0678 
View large
Table A8

Model criteria/goodness of Fit (USD/GBP)

StatisticValueStatisticValue
R-squared 0.961901 Mean dependent var 0.762102 
Adjusted R-squared 0.961020 S.D. dependent var 0.038186 
S.E. of regression 0.007539 Akaike info criterion −6.909746 
Sum squared resid 0.009833 Schwarz criterion −6.820371 
Log likelihood 619.9674 Hannan–Quinn criterion −6.873502 
F-statistic 1091.958 Durbin–Watson stat 1.904602 
Prob(F-statistic) 0.000000  
StatisticValueStatisticValue
R-squared 0.961901 Mean dependent var 0.762102 
Adjusted R-squared 0.961020 S.D. dependent var 0.038186 
S.E. of regression 0.007539 Akaike info criterion −6.909746 
Sum squared resid 0.009833 Schwarz criterion −6.820371 
Log likelihood 619.9674 Hannan–Quinn criterion −6.873502 
F-statistic 1091.958 Durbin–Watson stat 1.904602 
Prob(F-statistic) 0.000000  
View large
Table A9

Autocorrelation test (USD/GBP)

ACPACQ-StatProb*
1 0.135 0.135 3.2888 0.070 
2 −0.024 −0.043 3.3968 0.183 
3 −0.018 −0.009 3.4588 0.326 
4 0.075 0.079 4.4899 0.344 
5 0.050 0.028 4.9501 0.422 
6 0.134 0.131 8.2922 0.217 
ACPACQ-StatProb*
1 0.135 0.135 3.2888 0.070 
2 −0.024 −0.043 3.3968 0.183 
3 −0.018 −0.009 3.4588 0.326 
4 0.075 0.079 4.4899 0.344 
5 0.050 0.028 4.9501 0.422 
6 0.134 0.131 8.2922 0.217 
View large
Table A10

Granger causality test

Pairwise Granger causality tests 
Date: 04/16/25 Time: 11:45 
Sample: 6/23/2016 7/29/2022 
 Lags: 2  
Pairwise Granger causality tests 
Date: 04/16/25 Time: 11:45 
Sample: 6/23/2016 7/29/2022 
 Lags: 2  
ProbF-statisticObsNull hypothesis
0.8339 0.18178 177 EUR_GBP does not Granger Cause SCORE01 
0.0000 9.83723 SCORE01 does not Granger Cause EUR_GDP 
0.9337 0.06867 177 USD_TO_GBP does not Granger Cause SCORE01 
0.0270 3.69012 SCORE01 does not Granger Cause USD_TO_GDP 
0.5014 0.69318 177 CLOSE_PRICE does not Granger Cause SCORE01 
0.0000 10.2989 SCORE01 does not Granger Cause CLOSE_PRICE 
ProbF-statisticObsNull hypothesis
0.8339 0.18178 177 EUR_GBP does not Granger Cause SCORE01 
0.0000 9.83723 SCORE01 does not Granger Cause EUR_GDP 
0.9337 0.06867 177 USD_TO_GBP does not Granger Cause SCORE01 
0.0270 3.69012 SCORE01 does not Granger Cause USD_TO_GDP 
0.5014 0.69318 177 CLOSE_PRICE does not Granger Cause SCORE01 
0.0000 10.2989 SCORE01 does not Granger Cause CLOSE_PRICE 
View large
Figure A1
A graph shows trends from 6,000 to 7,600 and residuals from negative 150 to 450 across “2016” to “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The graph features two vertical axes. The vertical axis on the left ranges from negative 400 to 600 in increments of 200 units and corresponds to the line labeled “Residual”. The “Residual” line starts in “2016” at approximately negative 120, fluctuates with high-frequency volatility between negative 200 and 200 through “2021”, reaches a significant positive peak of approximately 450 in early “2022” at the “M 3” mark, and ends in “2022” at the “M 7” mark at approximately 80. The vertical axis on the right ranges from 5,600 to 8,000 in increments of 400 units and corresponds to the lines labeled “Actual” and “Fitted”. The “Actual” line starts in “2016” at approximately 6,050, increases to approximately 6,800 by “M 3” of “2021”, experiences a sharp, synchronized increase with the “Fitted” line to peak at approximately 7,600 in early “2022” at the “M 3” mark, and ends in “2022” at the “M 7” mark at approximately 7,400. The “Fitted” line follows a nearly identical path, starting in “2016” at approximately 6,000, increasing through “2021”, peaking in early “2022” at approximately 7,600, and ending in “2022” at approximately 7,450. Note: All numerical data values are approximated.

Actual, fitted, residual plot for the closing price

Figure A1
A graph shows trends from 6,000 to 7,600 and residuals from negative 150 to 450 across “2016” to “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The graph features two vertical axes. The vertical axis on the left ranges from negative 400 to 600 in increments of 200 units and corresponds to the line labeled “Residual”. The “Residual” line starts in “2016” at approximately negative 120, fluctuates with high-frequency volatility between negative 200 and 200 through “2021”, reaches a significant positive peak of approximately 450 in early “2022” at the “M 3” mark, and ends in “2022” at the “M 7” mark at approximately 80. The vertical axis on the right ranges from 5,600 to 8,000 in increments of 400 units and corresponds to the lines labeled “Actual” and “Fitted”. The “Actual” line starts in “2016” at approximately 6,050, increases to approximately 6,800 by “M 3” of “2021”, experiences a sharp, synchronized increase with the “Fitted” line to peak at approximately 7,600 in early “2022” at the “M 3” mark, and ends in “2022” at the “M 7” mark at approximately 7,400. The “Fitted” line follows a nearly identical path, starting in “2016” at approximately 6,000, increasing through “2021”, peaking in early “2022” at approximately 7,600, and ending in “2022” at approximately 7,450. Note: All numerical data values are approximated.

Actual, fitted, residual plot for the closing price

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Figure A2
A line graph shows “Residual”, “Actual”, and “Fitted” data with a sharp increase in values at the start of “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The graph features two vertical axes. The vertical axis on the left ranges from negative 400 to 600 in increments of 200 units and corresponds to the line labeled “Residual”. The “Residual” line is positioned in the lower portion of the graph, fluctuating around the 0 baseline. It shows the most significant positive spike occurring at the beginning of “2022”, reaching nearly 500, followed by a sharp drop toward negative 200. The vertical axis on the right ranges from 5,600 to 8,000 in increments of 400 units and corresponds to the lines labeled “Actual” and “Fitted”. The “Actual” and “Fitted” lines are positioned in the upper portion of the graph and follow a closely aligned path. They begin at above 6,-00 in “2016”, fluctuate between 6,400 and 6,800 through “2021”, and then show a significant upward trend at the start of “2022”, peaking near 7,600 before stabilizing between 7,200 and 7,400. Note: All numerical data values are approximated.

Actual, fitted, residual plot for EUR/GBP

Figure A2
A line graph shows “Residual”, “Actual”, and “Fitted” data with a sharp increase in values at the start of “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The graph features two vertical axes. The vertical axis on the left ranges from negative 400 to 600 in increments of 200 units and corresponds to the line labeled “Residual”. The “Residual” line is positioned in the lower portion of the graph, fluctuating around the 0 baseline. It shows the most significant positive spike occurring at the beginning of “2022”, reaching nearly 500, followed by a sharp drop toward negative 200. The vertical axis on the right ranges from 5,600 to 8,000 in increments of 400 units and corresponds to the lines labeled “Actual” and “Fitted”. The “Actual” and “Fitted” lines are positioned in the upper portion of the graph and follow a closely aligned path. They begin at above 6,-00 in “2016”, fluctuate between 6,400 and 6,800 through “2021”, and then show a significant upward trend at the start of “2022”, peaking near 7,600 before stabilizing between 7,200 and 7,400. Note: All numerical data values are approximated.

Actual, fitted, residual plot for EUR/GBP

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Figure A3
A line graph shows “Residual”, “Actual”, and “Fitted” data with an upward trend in values at the start of “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The vertical axis on the left represents “Residual” values and ranges from negative .02 to .06 in increments of .02 units. The vertical axis on the right represents values for the other series and ranges from .65 to .85 in increments of .05 units. The “Residual” line is positioned in the lower portion of the graph, fluctuating around the .00 baseline. It shows various peaks and valleys corresponding to the fluctuations in the data, with a significant positive spike occurring at the beginning of “2022” reaching nearly .04, following a previous notable drop to negative .02. The “Actual” and “Fitted” lines are positioned in the upper portion of the graph and follow a closely aligned path. They begin at approximately .75 in “2016”, show a slight downward trend toward .70 through “2021”, and then show a significant upward trend at the start of “2022”, peaking near .85 before ending slightly lower. Note: All data numerical values are approximated.

Actual, fitted, residual plot for USD/GBP

Figure A3
A line graph shows “Residual”, “Actual”, and “Fitted” data with an upward trend in values at the start of “2022”.
View largeDownload slide
The line graph displays three data series across three time periods: “2016”, “2021”, and “2022”. The three series are identified in the legend at the bottom as “Residual”, “Actual”, and “Fitted”. The horizontal axis is marked with time intervals across the years “2016”, “2021”, and “2022”. The axis includes “M 7” and “M 8” for “2016”; “M 1”, “M 2”, and “M 3” for “2021”; and “M 3”, “M 6”, and “M 7” for “2022”. The vertical axis on the left represents “Residual” values and ranges from negative .02 to .06 in increments of .02 units. The vertical axis on the right represents values for the other series and ranges from .65 to .85 in increments of .05 units. The “Residual” line is positioned in the lower portion of the graph, fluctuating around the .00 baseline. It shows various peaks and valleys corresponding to the fluctuations in the data, with a significant positive spike occurring at the beginning of “2022” reaching nearly .04, following a previous notable drop to negative .02. The “Actual” and “Fitted” lines are positioned in the upper portion of the graph and follow a closely aligned path. They begin at approximately .75 in “2016”, show a slight downward trend toward .70 through “2021”, and then show a significant upward trend at the start of “2022”, peaking near .85 before ending slightly lower. Note: All data numerical values are approximated.

Actual, fitted, residual plot for USD/GBP

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