%?Time?Series?Trend?Detection?Tests
%?[?z?sl?lcl?ucl?]?=?trend（?y?dt?）
%?where?z?=?Mann-Kendall?Statistic
%?sl?=?Sen‘s?Slope?Estimate
%?lcl?=?Lower?Confidence?Limit?of?sl
%?ucl?=?Upper?Confidence?Limit?of?sl
%?y?=?Time?Series?of?Data
%?dt?=?Time?Interval?of?Data
function?[?z?sl?lcl?ucl?]?=?trendMK（?y?dt?）
n?=?length（?y?）;

%?Mann-Kendall?Test?for?N?>?40
disp（?‘Mann-Kendall?Test;‘?）;
if?n?disp（?‘WARNING?-?sould?be?more?than?40?points‘?）;
end;

%?calculate?statistic
s?=?0;
for?k?=?1:n-1
for?j?=?k+1:n
s?=?s?+?sign（?y（j）?-?y（k）?）;
end;
end;

%?variance?（?assuming?no?tied?groups?）
v?=?（?n?*?（?n?-?1?）?*?（?2?*?n?+?5?）?）?/?18;

%?test?statistic
if?s?==?0
z?=?0;
elseif?s?>?0
z?=?（?s?-?1?）?/?sqrt（?v?）;
else
z?=?（?s?+?1?）?/?sqrt（?v?）;
end;?

%?should?calculate?Normal?value?here
nor?=?1.96;
%?results
disp（?[?‘?n?=?‘?num2str（?n?）?]?）;
disp（?[?‘?Mean?Value?=?‘?num2str（?mean（?y?）?）?]?）;
disp（?[?‘?Z?statistic?=?‘?num2str（?z?）?]?）;
if?abs（?z?）?disp（?‘?No?significant?trend‘?）;
z?=?0;
elseif?z?>?0
disp（?‘?Upward?trend?detected‘?）;
else
disp（?‘?Downward?trend?detected‘?）;
end;
disp（?‘Sens?Nonparametric?Estimator:‘?）;

%?calculate?slopes
ndash?=?n?*?（?n?-?1?）?/?2;
s?=?zeros（?ndash?1?）;
i?=?1;
for?k?=?1:n-1
for?j?=?k+1:n
s（i）?=?（?y（j）?-?y（k）?）?/?（?j?-?k?）?/?dt;
i?=?i?+?1;
end;
end;

%?the?estimate
sl?=?median（?s?）;
disp（?[?‘?Slope?Estimate?=?‘?num2str（?sl?）?]?）;
%?variance?（?assuming?no?tied?groups?）
v?=?（?n?*?（?n?-?1?）?*?（?2?*?n?+?5?）?）?/?18;
m1?=?fix（?（?ndash?-?nor?*?sqrt（?v?）?）?/?2?）;
m2?=?fix（?（?ndash?+?nor?*?sqrt（?v?）?）?/?2?）;
s?=?sort（?s?）;
lcl?=?s（?m1?）;
ucl?=?s（?m2?+?1?）;
disp（?[?‘?Lower?Confidence?Limit?=?‘?...
num2str（?lcl?）?]?）;
disp（?[?‘?Upper?Confidence?Limit?=?‘?...
num2str（?ucl?）?]?）;

?屬性????????????大小?????日期????時間???名稱
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?????文件????????1812??2015-04-11?20:36??trendMK.m