Timeseriesauto$-$correlation. SupposetheT$-$vectorxisanon$-$constanttimeseries,with xt thevalueattime$($orperiod$)$ t$.$ Let$=(1$Tx$)/$Tdenote itsmeanvalue. TheautocorrelationofxisthefunctionR$(\backslash$tau $),$definedfor$\backslash$tau $=0,1,...$asthecorrelationcoefficient ofthetwovectors$($x$,1\backslash$tau $)$and$(1\backslash$tau $,$x$).($Thesubscript$\backslash$tau denotesthelengthoftheones vector.$)$ Bothof thesevectorsalsohavemean$.$ Roughlyspeaking,R$(\backslash$tau $)$ tellsushow correlatedthetimeseries iswithaversionof itself laggedorshiftedby$\backslash$tau periods. $($The argument$\backslash$tau iscalledthelag.$)$