Moving average of semi-deviation

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.

Answer 1

[Image Analyst]

What is the definition of " semi-deviation"?

If you mean "Standard Deviation" then try stdfilt() or movstd().

[Image Analyst]

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));

Answer 2

[N/A]

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?

Answer 3

[Star Strider]

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.

Answer 4

[N/A]

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

[Star Strider]

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]

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.