function?[cortimelowup]=lag_corr_sig（data1data2alp）

%%%?a?simple?function?for?caculate?the?lag?correlation?of?two?timeseries
%
%?inputs:
%?data1?and?data2?are?two?time?series.
%?alp?:?（Optioal）?A?number?between?0?and?1?to?specify?a?confidence?level
%?of?100*（1?-?alpha）%.?Default?is?0.05?for?95%?confidence?intervals.
%?outputs:
%?cor:?the?correlation?of?data1?and?tata2
%?time:?lag?and?lead?time?for?data1?and?data2.
%?low:?lower?bounds?for?a??confidence?interval?for?each?coefficient?if?
%?nargin?is?2?then?the?interval?level?is?95%?for?default.
%?up:?uper?bounds?for?a?confidence?interval?for?each?coefficient.
%
%?Example
%?x=rand（1100）;y=rand（1100）;
%?[cortimelowup]=lag_corr_sig（xy）;
%?plot（timecor）;errorbar（time（1:10:end）cor（1:10:end）low（1:10:end）up（1:1
%?0：end））;
%?or?you?can?use?the?simple?output?just?calculate?the?lag?correlation
%?[cortimelowup]=lag_corr_sig（xy）;plot（timecor）;
len=length（data1）;
lag_time=floor（[len/3]）;%usually?the?lagtime?is?1/3?of?the?whole?length?of?the?data.
cor=zeros（lag_time1）;p=zeros（lag_time1）;l=lag_time;
if?len~=length（data2）
????error（‘you?must?use?two?same?length?series‘）;
end
if?size（data11）????data1=data1‘;
????data2=data2‘;
end
if?nargin?==?2
????for?j=1:lag_time?%data1?lead?data2
????????ab=data1（1:len-j）;
????????ac=data2（j+1:len）;
????????avex=mean（ab）;avey=mean（ac）;
????????sx=sqrt（sum（（ab-avex）.^2）/（len-j））;sy=sqrt（sum（（ac-avey）.^2）/（len-j））;
????????cor1（j）=sum（（（ab-avex）/sx）.*（（ac-avey）/sy））/（len-j）;
????????if?nargout?==?4
????????????[RPlow_matup_mat]=corrcoef（abac）;
????????????low1（j）=low_mat（12）;up1（j）=up_mat（12）;
????????end
????????clear?ab?ac?sx
????end
????
????for?j=1:lag_time
????????ab=data1（j+1:len）;
????????ac=data2（1:len-j）;
????????avex=mean（ab）;avey=mean（ac）;
????????sx=sqrt（sum（（ab-avex）.^2）/（len-j））;sy=sqrt（sum（（ac-avey）.^2）/（len-j））;
????????cor2（j）=sum（（（ab-avex）/sx）.*（（ac-avey）/sy））/（len-j）