Tests for a unit root with a one-time break in the trend function.

The regression model for the unit root tests is defined in equations (4) and (6) in the Supporting Information. The symbols are defined as follows: Tb is the estimated time of the break; is the Perron-Yabu Exp-Wald statistic with 5% trimming; k is the number of lagged differences added to correct for serial autocorrelation; , are the regression coefficients of the slope of the trend function and , the corresponding t-statistic values. Bold numbers denote statistical significance at 5% levels. is the post-break slope and is the percent difference with respect to the observed global temperature. is the sum of the first order autoregressive coefficients and is the Kim-Perron unit root test statistic.
a, b, cdenotes statistical significance at the 1%, 5% and 10%, respectively (for , for critical values taken from [21], Table 2.b; Kim-Perron unit root test critical values taken from [39], Table 1). Results for Observed taken from [6].