Hello all ,
I have four stochastic matrix, and I want to estimate (or mesure) the correlation beteween them?
Is Khi-deux test for indepence can be used? tests based on distance or what kind of tests ?
Thanks
First, the terminology - "stochastic matrices" might have three (or more) meanings:
1. matrices whose all raws are probability distributions
2. matrices with random entries (comp: "stochastic processes")
3. matrices appearing as a rsult of random perturbation from one "true" matrix
In the first case the notion "correlation" should be specifically defined; perhaps someone knows an example?
the second case is less free of freedom, but few rules are to be followed, e.g. it should be built (I think) of correlations of every entry of the first matrix with every entry of the second matrix.
the third case is probably the closes to the subject of the question; then probably the goal is to discover by statistical or approximative methods the similarity betwen the given matrices.
Each case requires more details about the problem.
Waiting for a response,
Joachim
Thank you very much Joachim Domsta and Paul Marcoux
for your responses,Yes, in fact I have data set of three financial markets , by which I realized an ARDL (cointegration approach), I found a long term relationships among them, but I treid to factorize the data set into four states fo each variable, so I found a new sequential data set, then, I fitted a Markov chain model to each new set, finally, three stochastix matrices have been estimated, so, following your suggestion dears: Joachim Domsta and Paul Marcoux
, is a khi-squared test sufficient to estimate independance (correlation) between these matrices ?Thanks
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