Spatio-temporal autocorrelation measures for nonstationary series: A new temporally detrended spatio-temporal Moran's index

•Temporally detrended global and local spatio-temporal Moran's indexes are defined.•Effects of timescale and timelag on spatio-temporal Moran's index are analyzed.•Moran's scatter plot is extended.•Statistical test of temporally detrended spatio-temporal Moran's index is taken.

In order to measure the spatio-temporal autocorrelation's degree for spatio-temporal nonstationary series, the new temporally detrended global and local spatio-temporal Moran's indexes (TDGSTI and TDLSTI) are proposed. The implementation of the new Moran's indexes is illustrated through artificial and real examples. Analyses of the influencing factors on TDGSTI are performed. A statistical test of TDGSTI is taken. The Moran's scatter plot, which discloses the spatio-temporal cluster pattern's characteristics and pattern's change, is extended. TDGSTI is found to reveal the autocorrelation level of spatio-temporal objects. For a positive TDGSTI, the higher the TDGSTI, the higher the autocorrelation level, and vice versa. TDGSTI is closely related to time-scale s, time-lag h   and spatio-temporal weight matrix. For s≫hs≫h, TDGSTI is significant, while for s∼hs∼h and s