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Moving average of semi-deviation

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rb250660
rb250660 2016-6-15
评论： Chris Turnes 2016-6-17
Hello,
I am trying to calculate the moving average of the semi-deviation of 1 column of data. I have been able to find a semi-deviation add-in but cannot find anything about making a moving average of the semi-deviation.
Any help appreciated.

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回答（4 个）

Image Analyst
Image Analyst 2016-6-15
What is the definition of " semi-deviation"?
If you mean "Standard Deviation" then try stdfilt() or movstd().
  1 个评论
Image Analyst
Image Analyst 2016-6-16
If you have a column vector of data and want the sd of data below the mean, just to
theMean = mean(data);
semiDeviation = std(data(data<theMean));

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rb250660
rb250660 2016-6-16
I found this script for semi-deviation: http://www.mathworks.com/matlabcentral/fileexchange/45251-semideviation
The definition is here: http://www.investopedia.com/terms/s/semideviation.asp
Basically is measures the standard deviation of the values that fall below the mean only.
I guess I can use the script I found and run it through a loop to get the moving average. How would I do this?
Star Strider
Star Strider 2016-6-16
I wrote my own function from your link and implemented an unfortunately inefficient filter to get the moving semideviation (using my own semideviation function):
semidev = @(x) sqrt(sum((mean(x(:)) - x(x(:) < mean(x(:)))).^2) / length(x(:)));
intvl = 10; % Index Interval For Moving Average
t = 1:100; % Time Vector
data = randn(1, 100); % Create Data
datav = [data, data(end-intvl+1:end)]; % ‘Pad’ ‘data’ With Repeat End Data
for k1 = 1:length(datav)-intvl;
wndw = k1:k1+intvl; % Subscript ‘Window’
sv(wndw) = semidev(datav(wndw)); % Calculate Semideviation Over ‘Window’
end
sv = sv(1:length(data)); % Trim To Correct Length
figure(1)
plot(t, data, 'bp')
hold on
plot(t, sv, '-r')
hold off
grid
It runs. I’ll let you determine if it produces the correct results.
rb250660
rb250660 2016-6-17
Thanks for the reply Star Strider. After some thought and further reading I propose the following code.
intvl = 10; % Index Interval For Moving Average
t = 1:100; % Time Vector
data = randn(1, 100); % Create Data
data_movmean = movmean( data, [intvl, 0] ); % Moving average of data
data_ds = data; % Set up downside dta array
data_ds( data > data_movmean ) = 0; % Modify downside data - zero values above mean
data_movdsstd = movstd( data_ds, [intvl, 0] ); % Semi-deviation
figure( 1 )
plot( t, data, 'bp' )
hold on
plot( t, data_movdsstd, '-r' )
hold off
grid
  2 个评论
Star Strider
Star Strider 2016-6-17
If it gives you the result you want, go for it!
I based my anonymous function code on the expression you linked to. It should give you the result you want, since all the x-values meeting the criteria are set to their appropriate values, and those that do not meet the criteria are set to zero by default anyway.
Chris Turnes
Chris Turnes 2016-6-17
The movstd call here will include the zeros in the calculation. From the definition, it sounds like you want to ignore those points, rather than treat them as zero. I think you could do this by:
data_ds( data > data_movmean ) = nan;
data_movdsstd = movstd( data_ds, [intvl, 0], 'omitnan' );
This should actually ignore those points rather than just consider them to be zero.

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