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We investigate the time trends in the maximum and minimum temperatures in the United States from 1895 to 2017 using techniques that allow for fractional integration in the detrended series. In doing so we get more accurate estimates of the trends than those obtained using standard methods that impose either stationarity I(0) or nonstationarity I(1). Our results reveal evidence of significant positive trends in both maximum and minimum temperatures, while the difference between them show a significant negative trend as a consequence of the higher increase in the minimum temperatures. Evidence of stationary long memory behavior is also found in the three series examined. [ABSTRACT FROM AUTHOR]