help needed to make transition probability matrix

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Mahesh 2015-7-27

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评论： Mahesh 2015-7-27

Dear all, I am brainstorming how to make transition probability matrix and had a code below. It does not work. It could be great to check my code and have a idea so that sum of all values in the matrix shall be one. My mind blocked after thinking a lot.

A = idxMA;
nmax = max(A);
nseries = numel(A);
states = zeros(nseries, nmax);
for i = 1:nmax
    states(:,i) = A==i;
end
jumpprob = zeros(nmax);
jmps = 1:nmax;
for i = 1:nmax
    X = jmps(i);
    for j = 1:njumps        
        Y = jmps(j);
        P = jumps(A, X, Y);
        jumpprob(i,j) = P/nseries;
    end
end
function [ P ] = jumps(data, X, Y )
%UNTITLED5 Summary of this function goes here
%   Detailed explanation goes here
    ndata = length(data);
    nstates = 0;
    for i = 1:ndata-1
        if data(i) > X && data(i+1) <= Y
            nstates = nstates + 1;
        end
    end
    P = nstates;
end

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Answer 1

John D'Errico 2015-7-27

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在 MATLAB Online 中打开

Um, no. A transition matrix does NOT have the sum of ALL values in the matrix as 1.

It must have the sum of every ROW of the matrix 1. There is a big difference. So as written below, T would be a valid transition matrix.

n = 6;
T = rand(n,n);
T = bsxfun(@times,T,1./sum(T,2))
T =
    0.19273      0.06588      0.22642       0.1874      0.16056      0.16702
    0.24566      0.14832      0.13164      0.26023      0.20551    0.0086335
   0.035665      0.26892      0.22476      0.18417      0.20871     0.077775
    0.36619      0.38684     0.056885     0.014318      0.15725     0.018511
    0.22476     0.056021      0.14991      0.30181      0.23298     0.034524
    0.02493      0.24807      0.23405      0.23872     0.043754      0.21047

The sum of the probabilities to move from any given state to one of the other states must be 1. So the sum of each row is 1, as I said it must be.

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Mahesh 2015-7-27

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Well thanks for the clue. But I am having problem with calculating matrix T. For that I have data

A = [2  2  2  2  2  2  7  7  7  7  7  7  7  7  7  4  4  4  4  4  4  10  10  10  10  1  1  1  1  1  6  6  5  5  5  9  9  9  9  9  9  9  9  3  3  3  3  9  3  3  8  8  8  8  8]
I hope it works for you to make me clear

Mahesh 2015-7-27

在 MATLAB Online 中打开

Moreover I got the matrix with all elements of last row is zeros. I tested with other set same thing happens.

jumpprob = [
18  21  22  31  36  45  49
13  16  17  25  30  39  43
9  12  13  21  25  33  37
4  7  8  16  20  28  31
4  5  6  14  18  25  28
4  4  4  12  16  23  26
3  3  3  3  7  14  17
3  3  3  3  3  10  13
1  1  1  1  1  1  4
0  0  0  0  0  0  0]