Exponentioal Moving Variance and the standard Variance comparison

EMV_Var_Compare.m

%==========================================================================
%   Exponentioal Moving Variance and the standard Variance comparison
%   Created by: Tiantian Xie (Dec. 10th, 2018)
%==========================================================================

clear;
close all;
NumberOfSamples = 500;
X = rand(NumberOfSamples,1);
WindowSize = 25;

% calculate the correct variance
for i=1:(NumberOfSamples-WindowSize+1)
    Slice =X(i:i+WindowSize-1);
    YVar(WindowSize-1+i) = var(Slice);
end

% calculate exponential moving variance
Mu=0;
V =0;
Alpha = 0.04;

for i=1:NumberOfSamples
    %ref:http://people.ds.cam.ac.uk/fanf2/hermes/doc/antiforgery/stats.pdf
    Diff = X(i)-Mu;
    Incr = Alpha*Diff;
    Mu = Mu + Incr;
    V = (1-Alpha)*(V+Incr*Diff);
    YEMV(i) = V;
end

% draw the plot
figure('Position',[0,0,800,400]);

plot(1:NumberOfSamples,YVar,1:NumberOfSamples,YEMV,'linewidth',2);
set(gca,'FontSize',20)
xlabel('Sample');
ylabel('Variance');
title('Exponential moving variance  v.s. variance');
L=legend('VAR ($N=25$)','EMV ($\alpha=0.04$)');
set(L, 'interpreter', 'latex');