Question

this is an update to the previous question that I had about locating peaks and troughs. The previous question was this:

peaks and troughs in MATLAB (but with corresponding definition of a peak and trough)

This time around, I did the suggested answer, but I think there is still something wrong with the final algorithm. Can you please tell me what I did wrong in my code? Thanks.

function [vectpeak, vecttrough]=peaktroughmodified(x,cutoff)

% This function is a modified version of the algorithm used to identify
% peaks and troughs in a series of prices. This will be used to identify
% the head and shoulders algorithm. The function gives you two vectors:
% PEAKS - an indicator vector that identifies the peaks in the function,
% and TROUGHS - an indicator vector that identifies the troughs of the
% function. The input is the vector of exchange rate series, and the cutoff
% used for refining possible peaks and troughs.

% Finding all possible peaks and troughs of our vector.
[posspeak,possploc]=findpeaks(x);
[posstrough,posstloc]=findpeaks(-x);
posspeak=posspeak';
posstrough=posstrough';

% Initialize vector of peaks and troughs.
numobs=length(x);
prelimpeaks=zeros(numobs,1); 
prelimtroughs=zeros(numobs,1);
numpeaks=numel(possploc);
numtroughs=numel(posstloc);

% Indicator for possible peaks and troughs.
for i=1:numobs
    for j=1:numpeaks
        if i==possploc(j);
            prelimpeaks(i)=1;
        end
    end
end

for i=1:numobs
    for j=1:numtroughs
       if i==posstloc(j);
            prelimtroughs(i)=1;
       end
    end
end

% Vector that gives location.
location=1:1:numobs;
location=location';

% From the list of possible peaks and troughs, find the peaks and troughs
% that fit Chang and Osler [1999] definition.
% "A peak is a local minimum at least x percent higher than the preceding
% trough, and a trough is a local minimum at least x percent lower than the
% preceding peak." [Chang and Osler, p.640]

% cutoffs
peakcutoff=1.0+cutoff; % cutoff for peaks
troughcutoff=1.0-cutoff; % cutoff for troughs


% First peak and first trough are initialized as previous peaks/troughs.

prevpeakloc=possploc(1);
prevtroughloc=posstloc(1);

% Initialize vectors of final peaks and troughs.
vectpeak=zeros(numobs,1);
vecttrough=zeros(numobs,1);

% We first check whether we start looking for peaks and troughs.
for i=1:numobs
    if prelimpeaks(i)==1;
       if i>prevtroughloc;
           ratio=x(i)/x(prevtroughloc);
           if ratio>peakcutoff;
               vectpeak(i)=1;
               prevpeakloc=location(i);
           else vectpeak(i)=0;
           end
       end
    elseif prelimtroughs(i)==1;
        if i>prevpeakloc;
            ratio=x(i)/x(prevpeakloc);
            if ratio<troughcutoff;
                vecttrough(i)=1;
                prevtroughloc=location(i);
            else vecttrough(i)=0;
            end
        end
    else
        vectpeak(i)=0;
        vecttrough(i)=0;
    end
end        
end

Answer 1

I just ran it, and it seems to work if you make this change:

peakcutoff= 1/cutoff; % cutoff for peaks
troughcutoff= cutoff; % cutoff for troughs

I tested it with the following code, with a cutoff of 0.1 (peaks must be 10 times larger than troughs), and it looks reasonable

x = randn(1,100).^2;
[vectpeak,vecttrough] = peaktroughmodified(x,0.1);
peaks = find(vectpeak);
troughs = find(vecttrough);
plot(1:100,x,peaks,x(peaks),'o',troughs,x(troughs),'o')

I strongly urge you to read up on vectorization in matlab. There are many wasted lines in your program, and it makes it difficult to read and will also make it very slow with big datasets. For instance, prelimpeaks and prelimtroughs can be completely defined without loops, in a single line for each:

prelimpeaks(possploc) = 1;
prelimtroughs(posstloc) = 1;